Ideals

Grzegorz Bancerek

Institute of Mathematics, Polish Academy of Sciences

Summary.

The dual concept to filters (see [1], [2]) i.e. ideals of a lattice is introduced.

MML Identifier: FILTER_2

Contents (PDF format)

1. Some Properties of the Restriction of Binary Operations
2. Closed Subsets of a Lattice
3. Ideals Generated by Subsets of a Lattice
4. Sublattices

Bibliography

[1] Grzegorz Bancerek. Filters --- part I. Journal of Formalized Mathematics, 2, 1990.

[2] Grzegorz Bancerek. Filters - part II. Quotient lattices modulo filters and direct product of two lattices. Journal of Formalized Mathematics, 3, 1991.

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

[4] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

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

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

[7] Jolanta Kamienska and Jaroslaw Stanislaw Walijewski. Homomorphisms of lattices, finite join and finite meet. Journal of Formalized Mathematics, 5, 1993.

[8] Andrzej Trybulec. Domains and their Cartesian products. Journal of Formalized Mathematics, 1, 1989.

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

[10] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.

[11] Andrzej Trybulec. Finite join and finite meet, and dual lattices. Journal of Formalized Mathematics, 2, 1990.

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

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

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