Journal of Formalized Mathematics
Volume 6, 1994
University of Bialystok
Copyright (c) 1994 Association of Mizar Users

Many Sorted Quotient Algebra


Malgorzata Korolkiewicz
Warsaw University, Bialystok

Summary.

This article introduces the construction of a many sorted quotient algebra. A few preliminary notions such as a many sorted relation, a many sorted equivalence relation, a many sorted congruence and the set of all classes of a many sorted relation are also formulated.

MML Identifier: MSUALG_4

The terminology and notation used in this paper have been introduced in the following articles [10] [14] [15] [3] [16] [5] [9] [4] [2] [1] [13] [11] [7] [12] [6] [8]

Contents (PDF format)

  1. Many Sorted Relation
  2. Many Sorted Quotient Algebra

Bibliography

[1] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.
[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[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] Malgorzata Korolkiewicz. Homomorphisms of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[7] Beata Madras. Product of family of universal algebras. Journal of Formalized Mathematics, 5, 1993.
[8] Beata Madras. Products of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[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] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[12] Andrzej Trybulec. Many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[13] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[14] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[15] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[16] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received May 6, 1994

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