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

On the Group of Automorphisms of Universal Algebra and Many Sorted Algebra


Artur Kornilowicz
Institute of Mathematics, Warsaw University, Bialystok

Summary.

The aim of the article is to check the compatibility of the automorphisms of universal algebras introduced in [10] and the corresponding concept for many sorted algebras introduced in [11].

MML Identifier: AUTALG_1

The terminology and notation used in this paper have been introduced in the following articles [15] [8] [21] [22] [5] [7] [6] [2] [4] [16] [17] [13] [19] [20] [1] [12] [3] [10] [14] [18] [11] [9]

Contents (PDF format)

  1. On the Group of Automorphisms of Universal Algebra
  2. Some Properties of Many Sorted Functions
  3. On the Group of Automorphisms of Many Sorted Algebra
  4. On the Relationship of Automorphisms of 1-sorted and Many Sorted Algebras

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] Ewa Burakowska. Subalgebras of the universal algebra. Lattices of subalgebras. Journal of Formalized Mathematics, 5, 1993.
[4] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[9] Adam Grabowski. The correspondence between homomorphisms of universal algebra \& many sorted algebra. Journal of Formalized Mathematics, 6, 1994.
[10] Malgorzata Korolkiewicz. Homomorphisms of algebras. Quotient universal algebra. Journal of Formalized Mathematics, 5, 1993.
[11] Malgorzata Korolkiewicz. Homomorphisms of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[12] Jaroslaw Kotowicz, Beata Madras, and Malgorzata Korolkiewicz. Basic notation of universal algebra. Journal of Formalized Mathematics, 4, 1992.
[13] Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski. Abelian groups, fields and vector spaces. Journal of Formalized Mathematics, 1, 1989.
[14] Beata Madras. Product of family of universal algebras. Journal of Formalized Mathematics, 5, 1993.
[15] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[16] Andrzej Trybulec. Function domains and Fr\aenkel operator. Journal of Formalized Mathematics, 2, 1990.
[17] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[18] Andrzej Trybulec. Many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[19] Wojciech A. Trybulec. Groups. Journal of Formalized Mathematics, 2, 1990.
[20] Wojciech A. Trybulec and Michal J. Trybulec. Homomorphisms and isomorphisms of groups. Quotient group. Journal of Formalized Mathematics, 3, 1991.
[21] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[22] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received December 13, 1994

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