Free Magmas
Identifieur interne : 000381 ( Istex/Checkpoint ); précédent : 000380; suivant : 000382Free Magmas
Auteurs : Marco Riccardi [Italie]Source :
- Formalized Mathematics [ 1426-2630 ] ; 2010-01-01.
English descriptors
- KwdEn :
- Canonical, Canonical homomorphism, Compatible equivalence relation, Cosets, Empty multiplicative magma, Equivalence kernel, Equivalence relation, Formalized mathematics, Free magma, Free magma sequence, Functor, Homomorphism, Magma, Multiplicative, Multiplicative magma, Natural number, Nite, Relators, Stable subset, Submagma, Subset.
- Teeft :
- Canonical, Canonical homomorphism, Compatible equivalence relation, Cosets, Empty multiplicative magma, Equivalence kernel, Equivalence relation, Formalized mathematics, Free magma, Free magma sequence, Functor, Homomorphism, Magma, Multiplicative, Multiplicative magma, Natural number, Nite, Relators, Stable subset, Submagma, Subset.
Abstract
This article introduces the free magma M(X) constructed on a set X [6]. Then, we formalize some theorems about M(X): if f is a function from the set X to a magma N, the free magma M(X) has a unique extension of f to a morphism of M(X) into N and every magma is isomorphic to a magma generated by a set X under a set of relators on M(X). In doing it, the article defines the stable subset under the law of composition of a magma, the submagma, the equivalence relation compatible with the law of composition and the equivalence kernel of a function. We also introduce some schemes on the recursive function.
Url:
DOI: 10.2478/v10037-010-0003-0
Affiliations:
Links toward previous steps (curation, corpus...)
Links to Exploration step
ISTEX:B276DA74AB4E0721CA582A692691AD3E7895799ALe document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Free Magmas</title>
<author wicri:is="90%"><name sortKey="Riccardi, Marco" sort="Riccardi, Marco" uniqKey="Riccardi M" first="Marco" last="Riccardi">Marco Riccardi</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:B276DA74AB4E0721CA582A692691AD3E7895799A</idno>
<date when="2010" year="2010">2010</date>
<idno type="doi">10.2478/v10037-010-0003-0</idno>
<idno type="url">https://api.istex.fr/document/B276DA74AB4E0721CA582A692691AD3E7895799A/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">002485</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">002485</idno>
<idno type="wicri:Area/Istex/Curation">002485</idno>
<idno type="wicri:Area/Istex/Checkpoint">000381</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000381</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Free Magmas</title>
<author wicri:is="90%"><name sortKey="Riccardi, Marco" sort="Riccardi, Marco" uniqKey="Riccardi M" first="Marco" last="Riccardi">Marco Riccardi</name>
<affiliation wicri:level="1"><country xml:lang="fr">Italie</country>
<wicri:regionArea>Via del Pero 102, 54038 Montignoso</wicri:regionArea>
<wicri:noRegion>54038 Montignoso</wicri:noRegion>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Formalized Mathematics</title>
<idno type="ISSN">1426-2630</idno>
<idno type="eISSN">1898-9934</idno>
<imprint><publisher>Versita</publisher>
<date type="published" when="2010-01-01">2010-01-01</date>
<biblScope unit="volume">18</biblScope>
<biblScope unit="issue">1</biblScope>
<biblScope unit="page" from="17">17</biblScope>
<biblScope unit="page" to="26">26</biblScope>
</imprint>
<idno type="ISSN">1426-2630</idno>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">1426-2630</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Canonical</term>
<term>Canonical homomorphism</term>
<term>Compatible equivalence relation</term>
<term>Cosets</term>
<term>Empty multiplicative magma</term>
<term>Equivalence kernel</term>
<term>Equivalence relation</term>
<term>Formalized mathematics</term>
<term>Free magma</term>
<term>Free magma sequence</term>
<term>Functor</term>
<term>Homomorphism</term>
<term>Magma</term>
<term>Multiplicative</term>
<term>Multiplicative magma</term>
<term>Natural number</term>
<term>Nite</term>
<term>Relators</term>
<term>Stable subset</term>
<term>Submagma</term>
<term>Subset</term>
</keywords>
<keywords scheme="Teeft" xml:lang="en"><term>Canonical</term>
<term>Canonical homomorphism</term>
<term>Compatible equivalence relation</term>
<term>Cosets</term>
<term>Empty multiplicative magma</term>
<term>Equivalence kernel</term>
<term>Equivalence relation</term>
<term>Formalized mathematics</term>
<term>Free magma</term>
<term>Free magma sequence</term>
<term>Functor</term>
<term>Homomorphism</term>
<term>Magma</term>
<term>Multiplicative</term>
<term>Multiplicative magma</term>
<term>Natural number</term>
<term>Nite</term>
<term>Relators</term>
<term>Stable subset</term>
<term>Submagma</term>
<term>Subset</term>
</keywords>
</textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">This article introduces the free magma M(X) constructed on a set X [6]. Then, we formalize some theorems about M(X): if f is a function from the set X to a magma N, the free magma M(X) has a unique extension of f to a morphism of M(X) into N and every magma is isomorphic to a magma generated by a set X under a set of relators on M(X). In doing it, the article defines the stable subset under the law of composition of a magma, the submagma, the equivalence relation compatible with the law of composition and the equivalence kernel of a function. We also introduce some schemes on the recursive function.</div>
</front>
</TEI>
<affiliations><list><country><li>Italie</li>
</country>
</list>
<tree><country name="Italie"><noRegion><name sortKey="Riccardi, Marco" sort="Riccardi, Marco" uniqKey="Riccardi M" first="Marco" last="Riccardi">Marco Riccardi</name>
</noRegion>
</country>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Istex/Checkpoint
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000381 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Checkpoint/biblio.hfd -nk 000381 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Mathematiques |area= BourbakiV1 |flux= Istex |étape= Checkpoint |type= RBID |clé= ISTEX:B276DA74AB4E0721CA582A692691AD3E7895799A |texte= Free Magmas }}
This area was generated with Dilib version V0.6.33. |