Relative annihilator-preserving congruence relations and relative annihilator-preserving homomorphisms in bounded distributive semilattices

Sergio A. Celani 1
  • 1 CONICET and Departamento de Matemáticas, Facultad de Ciencias Exactas, Universidad Nacional del Centro, Pinto 399, 7000, Tandil, Argentina

Abstract

In this paper we shall study a notion of relative annihilator-preserving congruence relation and relative annihilator-preserving homomorphism in the class of bounded distributive semilattices. We shall give a topological characterization of this class of semilattice homomorphisms. We shall prove that the semilattice congruences that are associated with filters are exactly the relative annihilator-preserving congruence relations.

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  • [1] Bezhanishvili G, and Jansana, R., Esakia Style Duality for Implicative Semilattices, Applied Categorical Structures, 2013, 21 (2), 181-208

  • [2] Chagrov, A., and Zakharyaschev M., Modal Logic, Oxford University Press, 1997

  • [3] Celani S. A and Calomino I. M., Some remarks on distributive semilattices, Comment. Math. Univ. Caroline, 2013, 54 (3), 407- 428

  • [4] Celani S. A., Remarks on annihilators preserving congruence relations, Mathematica Slovaca, 2012, 62 (3), 689-698

  • [5] Celani S. A., Topological representation of distributive semilattices, Scientiae Math. Japonicae online, 2003, (8), 41-51

  • [6] Celani, S. A., Representation of Hilbert algebras and implicative semilattices, Central European Journal of Mathematics, 2003, 4, 561-572

  • [7] Chajda I., Halaš R. and Kühr J., Semilattice Structures. Heldermann Verlag, Research and Exposition in Mathematics, 30, 2007

  • [8] Cornish, W. H., Normal lattices, Australian Mathematical Society. Journal. Pure Mathematics and Statistics, 1972, 14, 200-215

  • [9] Cornish W., Annulets and a-ideals in a distributive lattice, J. Austral Math. Soc., 1973, 15, 70-77

  • [10] Grätzer G., General Lattice Theory. Birkhäuser Verlag, 1998

  • [11] Janowitz M. F., Annihilator preserving congruence relations of lattices, Algebra Universalis,1975, 5 (1), 391–394

  • [12] Mandelker M., Relative annihilators in lattices, Duke Math. J., 1970, 37, 377–386

  • [13] Pawar S. P. and Lokhande A. D., Normal semilattices, Indian J. Pure and Appl. Math., 1998, 29, (12), 1245-1249

  • [14] Varlet J. C., Relative annihilators in semilattices, Bull. Austral. Math. Soc., 1973, 9, 169-185

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