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On free M V -algebras

Ján Jakubík (2003)

Czechoslovak Mathematical Journal

In the present paper we show that free M V -algebras can be constructed by applying free abelian lattice ordered groups.

On n × m-valued Łukasiewicz-Moisil algebras

Claudia Sanza (2008)

Open Mathematics

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...

On the lattice of n-filters of an LM n-algebra

Dumitru Buşneag, Florentina Chirteş (2007)

Open Mathematics

For an n-valued Łukasiewicz-Moisil algebra L (or LM n-algebra for short) we denote by F n(L) the lattice of all n-filters of L. The goal of this paper is to study the lattice F n(L) and to give new characterizations for the meet-irreducible and completely meet-irreducible elements on F n(L).

Ordered prime spectra of bounded D R l -monoids

Jiří Rachůnek (2000)

Mathematica Bohemica

Ordered prime spectra of Boolean products of bounded D R l -monoids are described by means of their decompositions to the prime spectra of the components.

Subdirectly irreducible MV-algebras

Hernando Gaitan (2003)

Czechoslovak Mathematical Journal

In this note we characterize the one-generated subdirectly irreducible MV-algebras and use this characterization to prove that a quasivariety of MV-algebras has the relative congruence extension property if and only if it is a variety.

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