The Correspondence Between Lattices of Subalgebras of Universal Algebras and Many Sorted Algebras

Adam Naumowicz

University of Bialystok

Agnieszka Julia Marasik

Warsaw University of Technology

Summary.

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.

MML Identifier: MSSUBLAT

Contents (PDF format)

1. Preliminaries
2. Some Properties of Subalgebras of Universal and Many Sorted Algebras
3. The Correspondence Between Lattices of Subalgebras of Universal and Many Sorted Algebras

Bibliography

[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.