Journal of Formalized Mathematics
Volume 5, 1993
University of Bialystok
Copyright (c) 1993
Association of Mizar Users
Subalgebras of the Universal Algebra. Lattices of Subalgebras

Ewa Burakowska

Warsaw University, Bialystok
Summary.

Introduces a definition of a subalgebra of a universal algebra. A notion
of similar algebras and basic operations on subalgebras such as a subalgebra
generated by a set, the intersection and the sum of two subalgebras were
introduced. Some basic facts concerning the above notions have been proved.
The article also contains the definition of a lattice of subalgebras of
a universal algebra.
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[5]
[10]
[11]
[3]
[1]
[8]
[4]
[6]
[12]
[2]
[7]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Binary operations.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Partial functions.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a nonempty sets.
Journal of Formalized Mathematics,
2, 1990.
 [7]
Jaroslaw Kotowicz, Beata Madras, and Malgorzata Korolkiewicz.
Basic notation of universal algebra.
Journal of Formalized Mathematics,
4, 1992.
 [8]
Beata Padlewska.
Families of sets.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [10]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [12]
Stanislaw Zukowski.
Introduction to lattice theory.
Journal of Formalized Mathematics,
1, 1989.
Received July 8, 1993
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