# On n × m-valued Łukasiewicz-Moisil algebras

Open Mathematics (2008)

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

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topClaudia 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 -

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