Journal of Formalized Mathematics
Volume 5, 1993
University of Bialystok
Copyright (c) 1993 Association of Mizar Users

Homomorphisms of Algebras. Quotient Universal Algebra


Malgorzata Korolkiewicz
Warsaw University, Bialystok

Summary.

The first part introduces homomorphisms of universal algebras and their basic properties. The second is concerned with the construction of a quotient universal algebra. The first isomorphism theorem is proved.

MML Identifier: ALG_1

The terminology and notation used in this paper have been introduced in the following articles [10] [11] [12] [14] [13] [3] [1] [5] [9] [7] [4] [8] [6] [2]

Contents (PDF format)

  1. Homomorphisms of Algebras
  2. Quotient Universal Algebra

Bibliography

[1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[2] Ewa Burakowska. Subalgebras of the universal algebra. Lattices of subalgebras. Journal of Formalized Mathematics, 5, 1993.
[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Binary operations applied to finite sequences. Journal of Formalized Mathematics, 2, 1990.
[7] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[8] Jaroslaw Kotowicz, Beata Madras, and Malgorzata Korolkiewicz. Basic notation of universal algebra. Journal of Formalized Mathematics, 4, 1992.
[9] Konrad Raczkowski and Pawel Sadowski. Equivalence relations and classes of abstraction. Journal of Formalized Mathematics, 1, 1989.
[10] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[11] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[12] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[13] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[14] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Journal of Formalized Mathematics, 1, 1989.

Received October 12, 1993

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