Geodesic
Modal Pseudocomplemented De Morgan Algebras
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 53 (2014) no. 1, pp. 65-79 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 03G99, 06D15, 06D30
Keywords: pseudocomplemented De Morgan algebras; Priestley spaces; discriminator varieties; congruences 
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Figallo, Aldo V.; Oliva, Nora; Ziliani, Alicia. Modal Pseudocomplemented De Morgan Algebras. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 53 (2014) no. 1, pp. 65-79. http://geodesic.mathdoc.fr/item/AUPO_2014_53_1_a4/

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