On <Emphasis Type="Italic">n</Emphasis> × <Emphasis Type="Italic">m</Emphasis>-valued ?ukasiewicz-Moisil algebras |
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Authors: | Claudia A Sanza |
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Institution: | (1) Universidad Nacional del Sur, Av. Alem 1253, 8000 Bahía Blanca, Argentina |
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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.
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Keywords: | n-valued Ł ukasiewicz-Moisil algebras Priestley spaces discriminator varieties congruences |
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