Volume 10, 1998

University of Bialystok

Copyright (c) 1998 Association of Mizar Users

**Adam Naumowicz**- University of Bialystok
**Agnieszka Julia Marasik**- Warsaw University of Technology

- The main goal of this paper is to show some properties of subalgebras of universal algebras and many sorted algebras, and then the isomorphic correspondence between lattices of such subalgebras.

- Preliminaries
- Some Properties of Subalgebras of Universal and Many Sorted Algebras
- The Correspondence Between Lattices of Subalgebras of Universal and Many Sorted Algebras

- [1]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [2]
Jozef Bialas.
Group and field definitions.
*Journal of Formalized Mathematics*, 1, 1989. - [3]
Ewa Burakowska.
Subalgebras of the universal algebra. Lattices of subalgebras.
*Journal of Formalized Mathematics*, 5, 1993. - [4]
Ewa Burakowska.
Subalgebras of many sorted algebra. Lattice of subalgebras.
*Journal of Formalized Mathematics*, 6, 1994. - [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.
A classical first order language.
*Journal of Formalized Mathematics*, 2, 1990. - [9]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a non-empty sets.
*Journal of Formalized Mathematics*, 2, 1990. - [10]
Jaroslaw Kotowicz, Beata Madras, and Malgorzata Korolkiewicz.
Basic notation of universal algebra.
*Journal of Formalized Mathematics*, 4, 1992. - [11]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [12]
Andrzej Trybulec.
Many-sorted sets.
*Journal of Formalized Mathematics*, 5, 1993. - [13]
Andrzej Trybulec.
Many sorted algebras.
*Journal of Formalized Mathematics*, 6, 1994. - [14]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [15]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [16]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [17]
Stanislaw Zukowski.
Introduction to lattice theory.
*Journal of Formalized Mathematics*, 1, 1989.

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