Free Magmas
Identifieur interne : 000425 ( Main/Exploration ); précédent : 000424; suivant : 000426Free 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:
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Le document en format XML
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<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>
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