Modal Pseudocomplemented De Morgan Algebras

Aldo V. Figallo; Nora Oliva; Alicia Ziliani

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2014)

  • Volume: 53, Issue: 1, page 65-79
  • ISSN: 0231-9721

Abstract

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Modal pseudocomplemented De Morgan algebras (or m p M -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 ∧ ( ∼ x ) * = ( ∼ ( x ∧ ( ∼ x ) * ) ) * . Firstly, a topological duality for these algebras is described and a characterization of m p M -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 m p M -congruences, the principal ones are described. In addition, it is proved that the variety of m p M -algebras is a discriminator variety and finally, the ternary discriminator polynomial is described.

How to cite

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Figallo, Aldo V., Oliva, Nora, and Ziliani, Alicia. "Modal Pseudocomplemented De Morgan Algebras." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 53.1 (2014): 65-79. <http://eudml.org/doc/261960>.

@article{Figallo2014,
abstract = {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.},
author = {Figallo, Aldo V., Oliva, Nora, Ziliani, Alicia},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {pseudocomplemented De Morgan algebras; Priestley spaces; discriminator varieties; congruences; pseudocomplemented De Morgan algebras; discriminator variety; topological duality; subdirectly irreducible mpM-algebra},
language = {eng},
number = {1},
pages = {65-79},
publisher = {Palacký University Olomouc},
title = {Modal Pseudocomplemented De Morgan Algebras},
url = {http://eudml.org/doc/261960},
volume = {53},
year = {2014},
}

TY - JOUR
AU - Figallo, Aldo V.
AU - Oliva, Nora
AU - Ziliani, Alicia
TI - Modal Pseudocomplemented De Morgan Algebras
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2014
PB - Palacký University Olomouc
VL - 53
IS - 1
SP - 65
EP - 79
AB - 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.
LA - eng
KW - pseudocomplemented De Morgan algebras; Priestley spaces; discriminator varieties; congruences; pseudocomplemented De Morgan algebras; discriminator variety; topological duality; subdirectly irreducible mpM-algebra
UR - http://eudml.org/doc/261960
ER -

References

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