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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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ISSN
1898-9934
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Volume 18, Issue 1 (Jan 2010)

Issues

Free Magmas

Marco Riccardi
  • Via del Pero 102, 54038 Montignoso, Italy
Published Online: 2011-01-05 | DOI: https://doi.org/10.2478/v10037-010-0003-0

Free Magmas

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.

  • [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.

  • [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.

  • [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.

About the article


Published Online: 2011-01-05

Published in Print: 2010-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-010-0003-0. Export Citation

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