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

Sergio A. Celani

Open Mathematics (2015)

  • Volume: 13, Issue: 1, page 165-177, electronic only
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Sergio A. Celani. "Relative annihilator-preserving congruence relations and relative annihilator-preserving homomorphisms in bounded distributive semilattices." Open Mathematics 13.1 (2015): 165-177, electronic only. <http://eudml.org/doc/268842>.

@article{SergioA2015,
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.},
author = {Sergio A. Celani},
journal = {Open Mathematics},
keywords = {Bounded distributive semilattices; Relative annihilator; Order-ideals; Congruences; bounded distributive semilattices; bounded distributive lattices; relative annihilators; order-ideals; semilattice congruences; semilattice homomorphisms},
language = {eng},
number = {1},
pages = {165-177, electronic only},
title = {Relative annihilator-preserving congruence relations and relative annihilator-preserving homomorphisms in bounded distributive semilattices},
url = {http://eudml.org/doc/268842},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Sergio A. Celani
TI - Relative annihilator-preserving congruence relations and relative annihilator-preserving homomorphisms in bounded distributive semilattices
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 165
EP - 177, electronic only
AB - 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.
LA - eng
KW - Bounded distributive semilattices; Relative annihilator; Order-ideals; Congruences; bounded distributive semilattices; bounded distributive lattices; relative annihilators; order-ideals; semilattice congruences; semilattice homomorphisms
UR - http://eudml.org/doc/268842
ER -

References

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  1. [1] Bezhanishvili G, and Jansana, R., Esakia Style Duality for Implicative Semilattices, Applied Categorical Structures, 2013, 21 (2), 181-208 [Crossref][WoS] Zbl1294.06005
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  4. [4] Celani S. A., Remarks on annihilators preserving congruence relations, Mathematica Slovaca, 2012, 62 (3), 689-698 [WoS][Crossref] Zbl1312.06002
  5. [5] Celani S. A., Topological representation of distributive semilattices, Scientiae Math. Japonicae online, 2003, (8), 41-51 
  6. [6] Celani, S. A., Representation of Hilbert algebras and implicative semilattices, Central European Journal of Mathematics, 2003, 4, 561-572 [Crossref][WoS] Zbl1034.03056
  7. [7] Chajda I., Halaš R. and Kühr J., Semilattice Structures. Heldermann Verlag, Research and Exposition in Mathematics, 30, 2007 
  8. [8] Cornish, W. H., Normal lattices, Australian Mathematical Society. Journal. Pure Mathematics and Statistics, 1972, 14, 200-215 Zbl0247.06009
  9. [9] Cornish W., Annulets and a-ideals in a distributive lattice, J. Austral Math. Soc., 1973, 15, 70-77 Zbl0274.06008
  10. [10] Grätzer G., General Lattice Theory. Birkhäuser Verlag, 1998 Zbl0909.06002
  11. [11] Janowitz M. F., Annihilator preserving congruence relations of lattices, Algebra Universalis,1975, 5 (1), 391–394 [Crossref][WoS] Zbl0333.06005
  12. [12] Mandelker M., Relative annihilators in lattices, Duke Math. J., 1970, 37, 377–386 [Crossref] Zbl0206.29701
  13. [13] Pawar S. P. and Lokhande A. D., Normal semilattices, Indian J. Pure and Appl. Math., 1998, 29, (12), 1245-1249 Zbl0921.06003
  14. [14] Varlet J. C., Relative annihilators in semilattices, Bull. Austral. Math. Soc., 1973, 9, 169-185 [Crossref] Zbl0258.06009

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