Free Magmas

Marco Riccardi

Formalized Mathematics (2010)

  • Volume: 18, Issue: 1, page 17-26
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Marco Riccardi. "Free Magmas." Formalized Mathematics 18.1 (2010): 17-26. <http://eudml.org/doc/266576>.

@article{MarcoRiccardi2010,
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.},
author = {Marco Riccardi},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {17-26},
title = {Free Magmas},
url = {http://eudml.org/doc/266576},
volume = {18},
year = {2010},
}

TY - JOUR
AU - Marco Riccardi
TI - Free Magmas
JO - Formalized Mathematics
PY - 2010
VL - 18
IS - 1
SP - 17
EP - 26
AB - 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.
LA - eng
UR - http://eudml.org/doc/266576
ER -

References

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