R
Identifieur interne : 001C20 ( Main/Merge ); précédent : 001C19; suivant : 001C21R
Auteurs : L. A. Skornyakov ; I. P. Mysovskikh ; A. A. Talalyan ; E. D. Solomentsev ; A. G. Sveshnikov ; V. A. Chuyanov ; A. L. Shmel In ; V. A. Andrunakievich ; R. A. Minlos ; K. Yu. Bulota ; L. V. Kuz In ; M. P. Mineev ; B. A. Sevast Anov ; N. N. Cnentsov ; R. L. Dobrushin ; V. V. Prelov ; Yu. V. Prokhorov ; A. M. Yaglom ; V. F. Kolchin ; V. I. Pagurova ; A. A. Borovkov ; M. S. Nikulin ; T. Yu. Popova ; O. A. Ivanova ; V. L. Popov ; V. E. Govorov ; M. V. Fedoryuk ; E. G. D Akonov ; K. P. Dolzhenko ; Viktor S. Kulikov ; D. Sullivan ; L. D. Kudryavtsev ; Val. S. Kulikov ; A. S. Rapinchuk ; A. V. Malyshev ; C. Dellacherie ; V. M. Babich ; A. V. Prokhorov ; N. Kh. Rozov ; P. C. Fife ; D. A. Gudkov ; D. A. Ponomarev ; V. E. Plisko ; S. A. Stepanov ; B. I. Golubov ; S. N. Artemov ; K. M. Millionshchikov ; V. M. Millionshchikov ; N. V. Belyakin ; V. A. Dushski ; P. J. Rousseeuw ; V. K. Domanski ; S. S. Goncharov ; A. N. Degtev ; S. G. Tankeev ; V. N. Grishin ; V. M. Millwnshchikov ; D. V. Alekseevski ; L. N. Shevrin ; V. F. Turchin ; A. V. Arkhangelski ; E. B. Vinberg ; E. P. Dolzhenko ; N. N. Vil Ams ; E. V. Solomentsev ; V. A. Buevich ; I. B. Vapnyarski ; U. A. Vladimirov ; N. N. Viil Ams ; A. B. Ivanov ; V. I. Danilov ; L. N. Shevnn ; A. P. Terekhin ; Yu. S. Ilyashenko ; A. V. Arkhangel Ski ; J. J. Volkov ; V. P. Platonov ; I. I. Volkov ; V. Ya. Arsenin ; A. N. Tikhonov ; A. S. Mishchenko ; A. P. Norden ; A. V. Mikhalev ; E. G. Sklyarenko ; D. D. Sokolov ; A. A. Ruzma Kin ; E. S. Nikolaev ; N. A. Karpova ; S. V. Yablonski ; Yu. K. Belyaev ; B. V. Gnedenko ; V. A. Sevast Anov ; S. A. Anikin ; M. Sh. Tsalenko ; A. L. Onishchik ; A. N. Rudakov ; C. M. Ringel ; L. M. Gluskin ; E. S. Lyapin ; A. I. Shtern ; A. V. Ro Ter ; N. M. Nagorny ; Yu. I. Merzlyakov ; E. A. Golubov ; A. P. Yuzhakov ; V. I. Sobolev ; L. V. Kuzmm ; M. I. Vo Tseknovski ; N. V. Butenin ; A. D. Bryuno ; I. V. Proskuryakov ; A. M. Nakhushev ; A. V. Arkhangel Ki ; V. S. Malakhovski ; E. L. Tonkov ; L. A. Sidorov ; I. Kh. Sabitov ; V. V. Shardurov ; A. A. Konyushkov ; F. D. Gakhov ; V. A. Il N ; A. M. Nakhyshev ; E. M. Chirka ; T. P. Lykashenko ; S. L. Krushkal ; Ü. Lumiste ; V. A. Toponogov ; Yu. D. Burago ; A. D. Aleksandrov ; V. N. Berestovski ; V. M. Tikhomirov ; T. P. Lukashenko ; V. F. Emel Anov ; Yu. B. Rudyak ; V. M. Kopytov ; A. N. Parshin ; Yu. A. Bakhturin ; K. A. ZhevlakovSource :
- Encyclopaedia of Mathematics ; 1995.
Abstract
Abstract: Regular Ring - A regular ring (in the sense of von Neumann) admitting an involutory anti-automorphism α→α* such that αα =0 implies α=0. An idempotent e of a *-regular ring is called a projector if e* =e. Every left (right) ideal of a *-regular ring is generated by a unique projector. One can thus speak of the lattice of projectors of a *-regular ring. If this lattice is complete, then it is a continuous geometry. A complemented modular lattice (cf. also Lattice with complements) having a homogeneous basis a 1 ..., a n , where n≥4, is an ortho-complemented lattice if and only if it is isomorphic to the lattice of projectors of some *-regular ring.
Url:
DOI: 10.1007/978-1-4899-3791-9_6
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<author><name sortKey="Mysovskikh, I P" sort="Mysovskikh, I P" uniqKey="Mysovskikh I" first="I. P." last="Mysovskikh">I. P. Mysovskikh</name>
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<author><name sortKey="Talalyan, A A" sort="Talalyan, A A" uniqKey="Talalyan A" first="A. A." last="Talalyan">A. A. Talalyan</name>
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<author><name sortKey="Solomentsev, E D" sort="Solomentsev, E D" uniqKey="Solomentsev E" first="E. D." last="Solomentsev">E. D. Solomentsev</name>
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<author><name sortKey="Sveshnikov, A G" sort="Sveshnikov, A G" uniqKey="Sveshnikov A" first="A. G." last="Sveshnikov">A. G. Sveshnikov</name>
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<author><name sortKey="Chuyanov, V A" sort="Chuyanov, V A" uniqKey="Chuyanov V" first="V. A." last="Chuyanov">V. A. Chuyanov</name>
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<author><name sortKey="Shmel In, A L" sort="Shmel In, A L" uniqKey="Shmel In A" first="A. L." last="Shmel In">A. L. Shmel In</name>
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<author><name sortKey="Andrunakievich, V A" sort="Andrunakievich, V A" uniqKey="Andrunakievich V" first="V. A." last="Andrunakievich">V. A. Andrunakievich</name>
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<author><name sortKey="Minlos, R A" sort="Minlos, R A" uniqKey="Minlos R" first="R. A." last="Minlos">R. A. Minlos</name>
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<author><name sortKey="Bulota, K Yu" sort="Bulota, K Yu" uniqKey="Bulota K" first="K. Yu." last="Bulota">K. Yu. Bulota</name>
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<author><name sortKey="Kuz In, L V" sort="Kuz In, L V" uniqKey="Kuz In L" first="L. V." last="Kuz In">L. V. Kuz In</name>
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<author><name sortKey="Mineev, M P" sort="Mineev, M P" uniqKey="Mineev M" first="M. P." last="Mineev">M. P. Mineev</name>
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<author><name sortKey="Sevast Anov, B A" sort="Sevast Anov, B A" uniqKey="Sevast Anov B" first="B. A." last="Sevast Anov">B. A. Sevast Anov</name>
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<author><name sortKey="Cnentsov, N N" sort="Cnentsov, N N" uniqKey="Cnentsov N" first="N. N." last="Cnentsov">N. N. Cnentsov</name>
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<author><name sortKey="Dobrushin, R L" sort="Dobrushin, R L" uniqKey="Dobrushin R" first="R. L." last="Dobrushin">R. L. Dobrushin</name>
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<author><name sortKey="Prelov, V V" sort="Prelov, V V" uniqKey="Prelov V" first="V. V." last="Prelov">V. V. Prelov</name>
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<author><name sortKey="Prokhorov, Yu V" sort="Prokhorov, Yu V" uniqKey="Prokhorov Y" first="Yu. V." last="Prokhorov">Yu. V. Prokhorov</name>
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<author><name sortKey="Yaglom, A M" sort="Yaglom, A M" uniqKey="Yaglom A" first="A. M." last="Yaglom">A. M. Yaglom</name>
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<author><name sortKey="Kolchin, V F" sort="Kolchin, V F" uniqKey="Kolchin V" first="V. F." last="Kolchin">V. F. Kolchin</name>
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<author><name sortKey="Pagurova, V I" sort="Pagurova, V I" uniqKey="Pagurova V" first="V. I." last="Pagurova">V. I. Pagurova</name>
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<author><name sortKey="Borovkov, A A" sort="Borovkov, A A" uniqKey="Borovkov A" first="A. A." last="Borovkov">A. A. Borovkov</name>
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<author><name sortKey="Nikulin, M S" sort="Nikulin, M S" uniqKey="Nikulin M" first="M. S." last="Nikulin">M. S. Nikulin</name>
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<author><name sortKey="Popova, T Yu" sort="Popova, T Yu" uniqKey="Popova T" first="T. Yu." last="Popova">T. Yu. Popova</name>
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<author><name sortKey="Ivanova, O A" sort="Ivanova, O A" uniqKey="Ivanova O" first="O. A." last="Ivanova">O. A. Ivanova</name>
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<author><name sortKey="Popov, V L" sort="Popov, V L" uniqKey="Popov V" first="V. L." last="Popov">V. L. Popov</name>
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<author><name sortKey="Govorov, V E" sort="Govorov, V E" uniqKey="Govorov V" first="V. E." last="Govorov">V. E. Govorov</name>
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<author><name sortKey="Fedoryuk, M V" sort="Fedoryuk, M V" uniqKey="Fedoryuk M" first="M. V." last="Fedoryuk">M. V. Fedoryuk</name>
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<author><name sortKey="D Akonov, E G" sort="D Akonov, E G" uniqKey="D Akonov E" first="E. G." last="D Akonov">E. G. D Akonov</name>
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<author><name sortKey="Dolzhenko, K P" sort="Dolzhenko, K P" uniqKey="Dolzhenko K" first="K. P." last="Dolzhenko">K. P. Dolzhenko</name>
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<author><name sortKey="Kulikov, Viktor S" sort="Kulikov, Viktor S" uniqKey="Kulikov V" first="Viktor S." last="Kulikov">Viktor S. Kulikov</name>
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<author><name sortKey="Sullivan, D" sort="Sullivan, D" uniqKey="Sullivan D" first="D." last="Sullivan">D. Sullivan</name>
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<author><name sortKey="Kudryavtsev, L D" sort="Kudryavtsev, L D" uniqKey="Kudryavtsev L" first="L. D." last="Kudryavtsev">L. D. Kudryavtsev</name>
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<author><name sortKey="Kulikov, Val S" sort="Kulikov, Val S" uniqKey="Kulikov V" first="Val. S." last="Kulikov">Val. S. Kulikov</name>
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<author><name sortKey="Rapinchuk, A S" sort="Rapinchuk, A S" uniqKey="Rapinchuk A" first="A. S." last="Rapinchuk">A. S. Rapinchuk</name>
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<author><name sortKey="Malyshev, A V" sort="Malyshev, A V" uniqKey="Malyshev A" first="A. V." last="Malyshev">A. V. Malyshev</name>
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<author><name sortKey="Dellacherie, C" sort="Dellacherie, C" uniqKey="Dellacherie C" first="C." last="Dellacherie">C. Dellacherie</name>
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<author><name sortKey="Babich, V M" sort="Babich, V M" uniqKey="Babich V" first="V. M." last="Babich">V. M. Babich</name>
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<author><name sortKey="Prokhorov, A V" sort="Prokhorov, A V" uniqKey="Prokhorov A" first="A. V." last="Prokhorov">A. V. Prokhorov</name>
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<author><name sortKey="Rozov, N Kh" sort="Rozov, N Kh" uniqKey="Rozov N" first="N. Kh." last="Rozov">N. Kh. Rozov</name>
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<author><name sortKey="Gudkov, D A" sort="Gudkov, D A" uniqKey="Gudkov D" first="D. A." last="Gudkov">D. A. Gudkov</name>
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<author><name sortKey="Ponomarev, D A" sort="Ponomarev, D A" uniqKey="Ponomarev D" first="D. A." last="Ponomarev">D. A. Ponomarev</name>
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<author><name sortKey="Plisko, V E" sort="Plisko, V E" uniqKey="Plisko V" first="V. E." last="Plisko">V. E. Plisko</name>
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<author><name sortKey="Stepanov, S A" sort="Stepanov, S A" uniqKey="Stepanov S" first="S. A." last="Stepanov">S. A. Stepanov</name>
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<author><name sortKey="Golubov, B I" sort="Golubov, B I" uniqKey="Golubov B" first="B. I." last="Golubov">B. I. Golubov</name>
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<author><name sortKey="Artemov, S N" sort="Artemov, S N" uniqKey="Artemov S" first="S. N." last="Artemov">S. N. Artemov</name>
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<author><name sortKey="Millionshchikov, K M" sort="Millionshchikov, K M" uniqKey="Millionshchikov K" first="K. M." last="Millionshchikov">K. M. Millionshchikov</name>
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<author><name sortKey="Millionshchikov, V M" sort="Millionshchikov, V M" uniqKey="Millionshchikov V" first="V. M." last="Millionshchikov">V. M. Millionshchikov</name>
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<author><name sortKey="Belyakin, N V" sort="Belyakin, N V" uniqKey="Belyakin N" first="N. V." last="Belyakin">N. V. Belyakin</name>
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<author><name sortKey="Dushski, V A" sort="Dushski, V A" uniqKey="Dushski V" first="V. A." last="Dushski">V. A. Dushski</name>
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<author><name sortKey="Rousseeuw, P J" sort="Rousseeuw, P J" uniqKey="Rousseeuw P" first="P. J." last="Rousseeuw">P. J. Rousseeuw</name>
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<author><name sortKey="Domanski, V K" sort="Domanski, V K" uniqKey="Domanski V" first="V. K." last="Domanski">V. K. Domanski</name>
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<author><name sortKey="Goncharov, S S" sort="Goncharov, S S" uniqKey="Goncharov S" first="S. S." last="Goncharov">S. S. Goncharov</name>
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<author><name sortKey="Degtev, A N" sort="Degtev, A N" uniqKey="Degtev A" first="A. N." last="Degtev">A. N. Degtev</name>
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<author><name sortKey="Tankeev, S G" sort="Tankeev, S G" uniqKey="Tankeev S" first="S. G." last="Tankeev">S. G. Tankeev</name>
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<author><name sortKey="Grishin, V N" sort="Grishin, V N" uniqKey="Grishin V" first="V. N." last="Grishin">V. N. Grishin</name>
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<author><name sortKey="Millwnshchikov, V M" sort="Millwnshchikov, V M" uniqKey="Millwnshchikov V" first="V. M." last="Millwnshchikov">V. M. Millwnshchikov</name>
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<author><name sortKey="Alekseevski, D V" sort="Alekseevski, D V" uniqKey="Alekseevski D" first="D. V." last="Alekseevski">D. V. Alekseevski</name>
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<author><name sortKey="Shevrin, L N" sort="Shevrin, L N" uniqKey="Shevrin L" first="L. N." last="Shevrin">L. N. Shevrin</name>
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<author><name sortKey="Turchin, V F" sort="Turchin, V F" uniqKey="Turchin V" first="V. F." last="Turchin">V. F. Turchin</name>
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<author><name sortKey="Arkhangelski, A V" sort="Arkhangelski, A V" uniqKey="Arkhangelski A" first="A. V." last="Arkhangelski">A. V. Arkhangelski</name>
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<author><name sortKey="Vinberg, E B" sort="Vinberg, E B" uniqKey="Vinberg E" first="E. B." last="Vinberg">E. B. Vinberg</name>
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<author><name sortKey="Dolzhenko, E P" sort="Dolzhenko, E P" uniqKey="Dolzhenko E" first="E. P." last="Dolzhenko">E. P. Dolzhenko</name>
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<author><name sortKey="Vil Ams, N N" sort="Vil Ams, N N" uniqKey="Vil Ams N" first="N. N." last="Vil Ams">N. N. Vil Ams</name>
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<author><name sortKey="Solomentsev, E V" sort="Solomentsev, E V" uniqKey="Solomentsev E" first="E. V." last="Solomentsev">E. V. Solomentsev</name>
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<author><name sortKey="Buevich, V A" sort="Buevich, V A" uniqKey="Buevich V" first="V. A." last="Buevich">V. A. Buevich</name>
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<author><name sortKey="Vapnyarski, I B" sort="Vapnyarski, I B" uniqKey="Vapnyarski I" first="I. B." last="Vapnyarski">I. B. Vapnyarski</name>
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<author><name sortKey="Vladimirov, U A" sort="Vladimirov, U A" uniqKey="Vladimirov U" first="U. A." last="Vladimirov">U. A. Vladimirov</name>
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<author><name sortKey="Viil Ams, N N" sort="Viil Ams, N N" uniqKey="Viil Ams N" first="N. N." last="Viil Ams">N. N. Viil Ams</name>
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<author><name sortKey="Ivanov, A B" sort="Ivanov, A B" uniqKey="Ivanov A" first="A. B." last="Ivanov">A. B. Ivanov</name>
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<author><name sortKey="Danilov, V I" sort="Danilov, V I" uniqKey="Danilov V" first="V. I." last="Danilov">V. I. Danilov</name>
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<author><name sortKey="Shevnn, L N" sort="Shevnn, L N" uniqKey="Shevnn L" first="L. N." last="Shevnn">L. N. Shevnn</name>
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<author><name sortKey="Terekhin, A P" sort="Terekhin, A P" uniqKey="Terekhin A" first="A. P." last="Terekhin">A. P. Terekhin</name>
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<author><name sortKey="Ilyashenko, Yu S" sort="Ilyashenko, Yu S" uniqKey="Ilyashenko Y" first="Yu. S." last="Ilyashenko">Yu. S. Ilyashenko</name>
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<author><name sortKey="Ski, A V Arkhangel" sort="Ski, A V Arkhangel" uniqKey="Ski A" first="A. V. Arkhangel" last="Ski">A. V. Arkhangel Ski</name>
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<author><name sortKey="Volkov, J J" sort="Volkov, J J" uniqKey="Volkov J" first="J. J." last="Volkov">J. J. Volkov</name>
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<author><name sortKey="Platonov, V P" sort="Platonov, V P" uniqKey="Platonov V" first="V. P." last="Platonov">V. P. Platonov</name>
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<author><name sortKey="Volkov, I I" sort="Volkov, I I" uniqKey="Volkov I" first="I. I." last="Volkov">I. I. Volkov</name>
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<author><name sortKey="Arsenin, V Ya" sort="Arsenin, V Ya" uniqKey="Arsenin V" first="V. Ya." last="Arsenin">V. Ya. Arsenin</name>
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<author><name sortKey="Tikhonov, A N" sort="Tikhonov, A N" uniqKey="Tikhonov A" first="A. N." last="Tikhonov">A. N. Tikhonov</name>
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<author><name sortKey="Mishchenko, A S" sort="Mishchenko, A S" uniqKey="Mishchenko A" first="A. S." last="Mishchenko">A. S. Mishchenko</name>
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<author><name sortKey="Norden, A P" sort="Norden, A P" uniqKey="Norden A" first="A. P." last="Norden">A. P. Norden</name>
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<author><name sortKey="Mikhalev, A V" sort="Mikhalev, A V" uniqKey="Mikhalev A" first="A. V." last="Mikhalev">A. V. Mikhalev</name>
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<author><name sortKey="Sklyarenko, E G" sort="Sklyarenko, E G" uniqKey="Sklyarenko E" first="E. G." last="Sklyarenko">E. G. Sklyarenko</name>
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<author><name sortKey="Sokolov, D D" sort="Sokolov, D D" uniqKey="Sokolov D" first="D. D." last="Sokolov">D. D. Sokolov</name>
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<author><name sortKey="Ruzma Kin, A A" sort="Ruzma Kin, A A" uniqKey="Ruzma Kin A" first="A. A." last="Ruzma Kin">A. A. Ruzma Kin</name>
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<author><name sortKey="Nikolaev, E S" sort="Nikolaev, E S" uniqKey="Nikolaev E" first="E. S." last="Nikolaev">E. S. Nikolaev</name>
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<author><name sortKey="Karpova, N A" sort="Karpova, N A" uniqKey="Karpova N" first="N. A." last="Karpova">N. A. Karpova</name>
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<author><name sortKey="Yablonski, S V" sort="Yablonski, S V" uniqKey="Yablonski S" first="S. V." last="Yablonski">S. V. Yablonski</name>
</author>
<author><name sortKey="Belyaev, Yu K" sort="Belyaev, Yu K" uniqKey="Belyaev Y" first="Yu. K." last="Belyaev">Yu. K. Belyaev</name>
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<author><name sortKey="Gnedenko, B V" sort="Gnedenko, B V" uniqKey="Gnedenko B" first="B. V." last="Gnedenko">B. V. Gnedenko</name>
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<author><name sortKey="Sevast Anov, V A" sort="Sevast Anov, V A" uniqKey="Sevast Anov V" first="V. A." last="Sevast Anov">V. A. Sevast Anov</name>
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<author><name sortKey="Anikin, S A" sort="Anikin, S A" uniqKey="Anikin S" first="S. A." last="Anikin">S. A. Anikin</name>
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<author><name sortKey="Tsalenko, M Sh" sort="Tsalenko, M Sh" uniqKey="Tsalenko M" first="M. Sh." last="Tsalenko">M. Sh. Tsalenko</name>
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<author><name sortKey="Onishchik, A L" sort="Onishchik, A L" uniqKey="Onishchik A" first="A. L." last="Onishchik">A. L. Onishchik</name>
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<author><name sortKey="Rudakov, A N" sort="Rudakov, A N" uniqKey="Rudakov A" first="A. N." last="Rudakov">A. N. Rudakov</name>
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<author><name sortKey="Ringel, C M" sort="Ringel, C M" uniqKey="Ringel C" first="C. M." last="Ringel">C. M. Ringel</name>
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<author><name sortKey="Gluskin, L M" sort="Gluskin, L M" uniqKey="Gluskin L" first="L. M." last="Gluskin">L. M. Gluskin</name>
</author>
<author><name sortKey="Lyapin, E S" sort="Lyapin, E S" uniqKey="Lyapin E" first="E. S." last="Lyapin">E. S. Lyapin</name>
</author>
<author><name sortKey="Shtern, A I" sort="Shtern, A I" uniqKey="Shtern A" first="A. I." last="Shtern">A. I. Shtern</name>
</author>
<author><name sortKey="Ro Ter, A V" sort="Ro Ter, A V" uniqKey="Ro Ter A" first="A. V." last="Ro Ter">A. V. Ro Ter</name>
</author>
<author><name sortKey="Nagorny, N M" sort="Nagorny, N M" uniqKey="Nagorny N" first="N. M." last="Nagorny">N. M. Nagorny</name>
</author>
<author><name sortKey="Merzlyakov, Yu I" sort="Merzlyakov, Yu I" uniqKey="Merzlyakov Y" first="Yu. I." last="Merzlyakov">Yu. I. Merzlyakov</name>
</author>
<author><name sortKey="Golubov, E A" sort="Golubov, E A" uniqKey="Golubov E" first="E. A." last="Golubov">E. A. Golubov</name>
</author>
<author><name sortKey="Yuzhakov, A P" sort="Yuzhakov, A P" uniqKey="Yuzhakov A" first="A. P." last="Yuzhakov">A. P. Yuzhakov</name>
</author>
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<idno type="RBID">ISTEX:EED6BC92C2027EF0625DF006B122BE966FAD80A4</idno>
<date when="1995" year="1995">1995</date>
<idno type="doi">10.1007/978-1-4899-3791-9_6</idno>
<idno type="url">https://api.istex.fr/document/EED6BC92C2027EF0625DF006B122BE966FAD80A4/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">003102</idno>
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<idno type="wicri:Area/Istex/Curation">003102</idno>
<idno type="wicri:Area/Istex/Checkpoint">001A01</idno>
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<idno type="wicri:Area/Main/Merge">001C20</idno>
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<monogr></monogr>
<series><title level="s">Encyclopaedia of Mathematics</title>
<imprint><date>1995</date>
</imprint>
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<front><div type="abstract" xml:lang="en">Abstract: Regular Ring - A regular ring (in the sense of von Neumann) admitting an involutory anti-automorphism α→α* such that αα =0 implies α=0. An idempotent e of a *-regular ring is called a projector if e* =e. Every left (right) ideal of a *-regular ring is generated by a unique projector. One can thus speak of the lattice of projectors of a *-regular ring. If this lattice is complete, then it is a continuous geometry. A complemented modular lattice (cf. also Lattice with complements) having a homogeneous basis a 1 ..., a n , where n≥4, is an ortho-complemented lattice if and only if it is isomorphic to the lattice of projectors of some *-regular ring.</div>
</front>
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