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On n × m-valued Łukasiewicz-Moisil algebras

100%

Sanza C.

Open Mathematics

2008

tom 6

nr 3

372-383

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.

A glimpse of deductive systems in algebra

52%

Buşneag D., Rudeanu S.

Open Mathematics

2010

tom 8

nr 4

688-705

The concept of a deductive system has been intensively studied in algebraic logic, per se and in connection with various types of filters. In this paper we introduce an axiomatization which shows how several resembling theorems that had been separately proved for various algebras of logic can be given unique proofs within this axiomatic framework. We thus recapture theorems already known in the literature, as well as new ones. As a by-product we introduce the class of pre-BCK algebras.

Ograniczanie wyników

2 Open Mathematics

1 Buşneag D.

1 Rudeanu S.

1 Sanza C.

1 2010

1 2008

Wyniki wyszukiwania

On n × m-valued Łukasiewicz-Moisil algebras

A glimpse of deductive systems in algebra