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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Chuyanov</name></author><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></author><author><name sortKey="Andrunakievich, V A" sort="Andrunakievich, V A" uniqKey="Andrunakievich V" first="V. A." last="Andrunakievich">V. A. Andrunakievich</name></author><author><name sortKey="Minlos, R A" sort="Minlos, R A" uniqKey="Minlos R" first="R. A." last="Minlos">R. A. Minlos</name></author><author><name sortKey="Bulota, K Yu" sort="Bulota, K Yu" uniqKey="Bulota K" first="K. Yu." last="Bulota">K. Yu. Bulota</name></author><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></author><author><name sortKey="Mineev, M P" sort="Mineev, M P" uniqKey="Mineev M" first="M. P." last="Mineev">M. P. Mineev</name></author><author><name sortKey="Sevast Anov, B A" sort="Sevast Anov, B A" uniqKey="Sevast Anov B" first="B. A." last="Sevast Anov">B. A. 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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></author><author><name sortKey="Gnedenko, B V" sort="Gnedenko, B V" uniqKey="Gnedenko B" first="B. V." last="Gnedenko">B. V. Gnedenko</name></author><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></author><author><name sortKey="Anikin, S A" sort="Anikin, S A" uniqKey="Anikin S" first="S. A." last="Anikin">S. A. Anikin</name></author><author><name sortKey="Tsalenko, M Sh" sort="Tsalenko, M Sh" uniqKey="Tsalenko M" first="M. Sh." last="Tsalenko">M. Sh. Tsalenko</name></author><author><name sortKey="Onishchik, A L" sort="Onishchik, A L" uniqKey="Onishchik A" first="A. L." last="Onishchik">A. L. Onishchik</name></author><author><name sortKey="Rudakov, A N" sort="Rudakov, A N" uniqKey="Rudakov A" first="A. N." last="Rudakov">A. N. Rudakov</name></author><author><name sortKey="Ringel, C M" sort="Ringel, C M" uniqKey="Ringel C" first="C. M." last="Ringel">C. M. Ringel</name></author><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><author><name sortKey="Sobolev, V I" sort="Sobolev, V I" uniqKey="Sobolev V" first="V. I." last="Sobolev">V. I. Sobolev</name></author><author><name sortKey="Kuzmm, L V" sort="Kuzmm, L V" uniqKey="Kuzmm L" first="L. V." last="Kuzmm">L. V. Kuzmm</name></author><author><name sortKey="Vo Tseknovski, M I" sort="Vo Tseknovski, M I" uniqKey="Vo Tseknovski M" first="M. I." last="Vo Tseknovski">M. I. Vo Tseknovski</name></author><author><name sortKey="Butenin, N V" sort="Butenin, N V" uniqKey="Butenin N" first="N. V." last="Butenin">N. V. Butenin</name></author><author><name sortKey="Bryuno, A D" sort="Bryuno, A D" uniqKey="Bryuno A" first="A. D." last="Bryuno">A. D. 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Kh." last="Sabitov">I. Kh. Sabitov</name></author><author><name sortKey="Shardurov, V V" sort="Shardurov, V V" uniqKey="Shardurov V" first="V. V." last="Shardurov">V. V. Shardurov</name></author><author><name sortKey="Konyushkov, A A" sort="Konyushkov, A A" uniqKey="Konyushkov A" first="A. A." last="Konyushkov">A. A. Konyushkov</name></author><author><name sortKey="Gakhov, F D" sort="Gakhov, F D" uniqKey="Gakhov F" first="F. D." last="Gakhov">F. D. Gakhov</name></author><author><name sortKey="Il N, V A" sort="Il N, V A" uniqKey="Il N V" first="V. A." last="Il N">V. A. Il N</name></author><author><name sortKey="Nakhyshev, A M" sort="Nakhyshev, A M" uniqKey="Nakhyshev A" first="A. M." last="Nakhyshev">A. M. Nakhyshev</name></author><author><name sortKey="Chirka, E M" sort="Chirka, E M" uniqKey="Chirka E" first="E. M." last="Chirka">E. M. Chirka</name></author><author><name sortKey="Lykashenko, T P" sort="Lykashenko, T P" uniqKey="Lykashenko T" first="T. P." last="Lykashenko">T. P. Lykashenko</name></author><author><name sortKey="Krushkal, S L" sort="Krushkal, S L" uniqKey="Krushkal S" first="S. L." last="Krushkal">S. L. Krushkal</name></author><author><name sortKey="Lumiste, U" sort="Lumiste, U" uniqKey="Lumiste U" first="Ü." last="Lumiste">Ü. Lumiste</name></author><author><name sortKey="Toponogov, V A" sort="Toponogov, V A" uniqKey="Toponogov V" first="V. A." last="Toponogov">V. A. Toponogov</name></author><author><name sortKey="Burago, Yu D" sort="Burago, Yu D" uniqKey="Burago Y" first="Yu. D." last="Burago">Yu. D. Burago</name></author><author><name sortKey="Aleksandrov, A D" sort="Aleksandrov, A D" uniqKey="Aleksandrov A" first="A. D." last="Aleksandrov">A. D. Aleksandrov</name></author><author><name sortKey="Berestovski, V N" sort="Berestovski, V N" uniqKey="Berestovski V" first="V. N." last="Berestovski">V. N. Berestovski</name></author><author><name sortKey="Tikhomirov, V M" sort="Tikhomirov, V M" uniqKey="Tikhomirov V" first="V. M." last="Tikhomirov">V. M. Tikhomirov</name></author><author><name sortKey="Lukashenko, T P" sort="Lukashenko, T P" uniqKey="Lukashenko T" first="T. P." last="Lukashenko">T. P. Lukashenko</name></author><author><name sortKey="Emel Anov, V F" sort="Emel Anov, V F" uniqKey="Emel Anov V" first="V. F." last="Emel Anov">V. F. Emel Anov</name></author><author><name sortKey="Rudyak, Yu B" sort="Rudyak, Yu B" uniqKey="Rudyak Y" first="Yu. B." last="Rudyak">Yu. B. Rudyak</name></author><author><name sortKey="Kopytov, V M" sort="Kopytov, V M" uniqKey="Kopytov V" first="V. M." last="Kopytov">V. M. Kopytov</name></author><author><name sortKey="Parshin, A N" sort="Parshin, A N" uniqKey="Parshin A" first="A. N." last="Parshin">A. N. Parshin</name></author><author><name sortKey="Bakhturin, Yu A" sort="Bakhturin, Yu A" uniqKey="Bakhturin Y" first="Yu. A." last="Bakhturin">Yu. A. Bakhturin</name></author><author><name sortKey="Zhevlakov, K A" sort="Zhevlakov, K A" uniqKey="Zhevlakov K" first="K. A." last="Zhevlakov">K. A. Zhevlakov</name></author></analytic><monogr></monogr><series><title level="s">Encyclopaedia of Mathematics</title><imprint><date>1995</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><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></TEI></record>Pour manipuler ce document sous Unix (Dilib)
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