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Remarks on annihilators preserving congruence relations
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Abstract
In this note we shall give some results on annihilators preserving congruence relations, or AP-congruences, in bounded distributive lattices. We shall give some new characterizations, and a topological interpretation of the notion of annihilator preserving congruences introduced in [JANOWITZ, M. F.: Annihilator preserving congruence relations of lattices, Algebra Universalis 5 (1975), 391–394]. As an application of these results, we shall prove that the quotient of a quasicomplemented lattice by means of a AP-congruence is a quasicomplemented lattice. Similarly, we will prove that the quotient of a normal latttice by means of a AP-congruence is also a normal lattice.
Title: Remarks on annihilators preserving congruence relations
Description:
Abstract
In this note we shall give some results on annihilators preserving congruence relations, or AP-congruences, in bounded distributive lattices.
We shall give some new characterizations, and a topological interpretation of the notion of annihilator preserving congruences introduced in [JANOWITZ, M.
F.
: Annihilator preserving congruence relations of lattices, Algebra Universalis 5 (1975), 391–394].
As an application of these results, we shall prove that the quotient of a quasicomplemented lattice by means of a AP-congruence is a quasicomplemented lattice.
Similarly, we will prove that the quotient of a normal latttice by means of a AP-congruence is also a normal lattice.
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