Remarks on annihilators preserving congruence relations |
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Authors: | Sergio A Celani |
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Institution: | 1.CONICET and Departamento de Matemàticas Facultad de Ciencias Exactas,Universidad Nacional del Centro,Tandil,Argentina |
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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. |
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