Introduction to Lattice Theory

Stanislaw Zukowski

Warsaw University, Bialystok

Supported by RPBP.III-24.C1.

Summary.

A lattice is defined as an algebra on a nonempty set with binary operations join and meet which are commutative and associative, and satisfy the absorption identities. The following kinds of lattices are considered: distributive, modular, bounded (with zero and unit elements), complemented, and Boolean (with complement). The article includes also theorems which immediately follow from definitions.

MML Identifier: LATTICES

Contents (PDF format)

Bibliography

[1] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.

[2] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

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