Lattice of Congruences in Many Sorted Algebra

Robert Milewski

Warsaw University, Bialystok

MML Identifier: MSUALG_5

Contents (PDF format)

1. More on Equivalence Relations
2. Lattice of Equivalence Relations
3. Many Sorted Equivalence Relations
4. Lattice of Many Sorted Equivalence Relations
5. Lattice of Congruences in Many Sorted Algebra

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.

[2] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.

[3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.

[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] Marek Chmur. The lattice of natural numbers and the sublattice of it. The set of prime numbers. Journal of Formalized Mathematics, 3, 1991.

[10] Malgorzata Korolkiewicz. Homomorphisms of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.

[11] Malgorzata Korolkiewicz. Many sorted quotient algebra. Journal of Formalized Mathematics, 6, 1994.

[12] Beata Madras. Products of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.

[13] Konrad Raczkowski and Pawel Sadowski. Equivalence relations and classes of abstraction. Journal of Formalized Mathematics, 1, 1989.

[14] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[15] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.

[16] Andrzej Trybulec. Many sorted algebras. Journal of Formalized Mathematics, 6, 1994.

[17] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.

[18] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[19] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[20] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

[21] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Journal of Formalized Mathematics, 1, 1989.

[22] Stanislaw Zukowski. Introduction to lattice theory. Journal of Formalized Mathematics, 1, 1989.