Journal of Formalized Mathematics
Volume 6, 1994
University of Bialystok
Copyright (c) 1994
Association of Mizar Users
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.
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[5]
[12]
[4]
[8]
[3]
[14]
[6]
[1]
[11]
[10]
[13]
[7]

Some Properties of the Restriction of Binary Operations

Closed Subsets of a Lattice

Ideals Generated by Subsets of a Lattice

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.
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Journal of Formalized Mathematics,
3, 1991.
 [7]
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Homomorphisms of lattices, finite join and finite meet.
Journal of Formalized Mathematics,
5, 1993.
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Journal of Formalized Mathematics,
1, 1989.
 [9]
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Tarski Grothendieck set theory.
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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.
Received October 24, 1994
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