# Free Magmas

Formalized Mathematics (2010)

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

## Access Full Article

top## Abstract

top## How to cite

topMarco 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

top- [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
- [2] Grzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990.
- [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
- [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
- [5] Józef Białas. Group and field definitions. Formalized Mathematics, 1(3):433-439, 1990.
- [6] Nicolas Bourbaki. Elements of Mathematics. Algebra I. Chapters 1-3. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1989. Zbl0673.00001
- [7] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
- [8] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
- [9] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
- [10] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
- [11] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
- [12] Małgorzata Korolkiewicz. Homomorphisms of algebras. Quotient universal algebra. Formalized Mathematics, 4(1):109-113, 1993.
- [13] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
- [14] Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.
- [15] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.
- [16] Andrzej Trybulec. Moore-Smith convergence. Formalized Mathematics, 6(2):213-225, 1997.
- [17] Wojciech A. Trybulec and Michał J. Trybulec. Homomorphisms and isomorphisms of groups. Quotient group. Formalized Mathematics, 2(4):573-578, 1991.
- [18] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
- [19] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.
- [20] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
- [21] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.