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Keywords:
pseudocomplemented De Morgan algebras; Priestley spaces; discriminator varieties; congruences
pseudocomplemented De Morgan algebras; Priestley spaces; discriminator varieties; congruences
Summary:
Modal pseudocomplemented De Morgan algebras (or $mpM$-algebras for short) are investigated in this paper. This new equational class of algebras was introduced by A. V. Figallo and P. Landini ([Figallo, A. V., Landini, P.: Notes on $4$-valued modal algebras Preprints del Instituto de Ciencias Básicas, Univ. Nac. de San Juan 1 (1990), 28–37.]) and they constitute a proper subvariety of the variety of all pseudocomplemented De Morgan algebras satisfying $x\wedge (\sim x)^\ast = (\sim (x\wedge (\sim x)^\ast ))^\ast $. Firstly, a topological duality for these algebras is described and a characterization of $mpM$-congruences in terms of special subsets of the associated space is shown. As a consequence, the subdirectly irreducible algebras are determined. Furthermore, from the above results on the $mpM$-congruences, the principal ones are described. In addition, it is proved that the variety of $mpM$-algebras is a discriminator variety and finally, the ternary discriminator polynomial is described.
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