On n × m-valued Łukasiewicz-Moisil algebras

Claudia Sanza

Open Mathematics (2008)

  • Volume: 6, Issue: 3, page 372-383
  • ISSN: 2391-5455

Abstract

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n×m-valued Łukasiewicz algebras with negation were introduced and investigated in [20, 22, 23]. These algebras constitute a non trivial generalization of n-valued Łukasiewicz-Moisil algebras and in what follows, we shall call them n×m-valued Łukasiewicz-Moisil algebras (or LM n×m -algebras). In this paper, the study of this new class of algebras is continued. More precisely, a topological duality for these algebras is described and a characterization of LM n×m -congruences in terms of special subsets of the associated space is shown. Besides, it is determined which of these subsets correspond to principal congruences. In addition, it is proved that the variety of LM n×m -algebras is a discriminator variety and as a consequence, certain properties of the congruences are obtained. Finally, the number of congruences of a finite LM n×m -algebra is computed.

How to cite

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Claudia Sanza. "On n × m-valued Łukasiewicz-Moisil algebras." Open Mathematics 6.3 (2008): 372-383. <http://eudml.org/doc/269521>.

@article{ClaudiaSanza2008,
abstract = {n×m-valued Łukasiewicz algebras with negation were introduced and investigated in [20, 22, 23]. These algebras constitute a non trivial generalization of n-valued Łukasiewicz-Moisil algebras and in what follows, we shall call them n×m-valued Łukasiewicz-Moisil algebras (or LM n×m -algebras). In this paper, the study of this new class of algebras is continued. More precisely, a topological duality for these algebras is described and a characterization of LM n×m -congruences in terms of special subsets of the associated space is shown. Besides, it is determined which of these subsets correspond to principal congruences. In addition, it is proved that the variety of LM n×m -algebras is a discriminator variety and as a consequence, certain properties of the congruences are obtained. Finally, the number of congruences of a finite LM n×m -algebra is computed.},
author = {Claudia Sanza},
journal = {Open Mathematics},
keywords = {n-valued Łukasiewicz-Moisil algebras; Priestley spaces; discriminator varieties; congruences},
language = {eng},
number = {3},
pages = {372-383},
title = {On n × m-valued Łukasiewicz-Moisil algebras},
url = {http://eudml.org/doc/269521},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Claudia Sanza
TI - On n × m-valued Łukasiewicz-Moisil algebras
JO - Open Mathematics
PY - 2008
VL - 6
IS - 3
SP - 372
EP - 383
AB - n×m-valued Łukasiewicz algebras with negation were introduced and investigated in [20, 22, 23]. These algebras constitute a non trivial generalization of n-valued Łukasiewicz-Moisil algebras and in what follows, we shall call them n×m-valued Łukasiewicz-Moisil algebras (or LM n×m -algebras). In this paper, the study of this new class of algebras is continued. More precisely, a topological duality for these algebras is described and a characterization of LM n×m -congruences in terms of special subsets of the associated space is shown. Besides, it is determined which of these subsets correspond to principal congruences. In addition, it is proved that the variety of LM n×m -algebras is a discriminator variety and as a consequence, certain properties of the congruences are obtained. Finally, the number of congruences of a finite LM n×m -algebra is computed.
LA - eng
KW - n-valued Łukasiewicz-Moisil algebras; Priestley spaces; discriminator varieties; congruences
UR - http://eudml.org/doc/269521
ER -

References

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