Monadic n × m -valued Łukasiewicz-Moisil algebras

A. V. Figallo; Claudia A. Sanza

Mathematica Bohemica (2012)

  • Volume: 137, Issue: 4, page 425-447
  • ISSN: 0862-7959

Abstract

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Here we initiate an investigation into the class m L M n × m of monadic n × m -valued Łukasiewicz-Moisil algebras (or m L M n × m -algebras), namely n × m -valued Łukasiewicz-Moisil algebras endowed with a unary operation. These algebras constitute a generalization of monadic n -valued Łukasiewicz-Moisil algebras. In this article, the congruences on these algebras are determined and subdirectly irreducible algebras are characterized. From this last result it is proved that m L M n × m is a discriminator variety and as a consequence, the principal congruences are characterized. Furthermore, the number of congruences of finite m L M n × m -algebras is computed. In addition, a topological duality for m L M n × m -algebras is described and a characterization of m L M n × m -congruences in terms of special subsets of the associated space is shown. Moreover, the subsets which correspond to principal congruences are determined. Finally, some functional representation theorems for these algebras are given and the relationship between them is pointed out.

How to cite

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Figallo, A. V., and Sanza, Claudia A.. "Monadic $n\times m$-valued Łukasiewicz-Moisil algebras." Mathematica Bohemica 137.4 (2012): 425-447. <http://eudml.org/doc/246958>.

@article{Figallo2012,
abstract = {Here we initiate an investigation into the class $mLM_\{n\times m\}$ of monadic $n\times m$-valued Łukasiewicz-Moisil algebras (or $mLM_\{n \times m\}$-algebras), namely $n\times m$-valued Łukasiewicz-Moisil algebras endowed with a unary operation. These algebras constitute a generalization of monadic $n$-valued Łukasiewicz-Moisil algebras. In this article, the congruences on these algebras are determined and subdirectly irreducible algebras are characterized. From this last result it is proved that $mLM_\{n\times m\}$ is a discriminator variety and as a consequence, the principal congruences are characterized. Furthermore, the number of congruences of finite $mLM_\{n \times m\}$-algebras is computed. In addition, a topological duality for $mLM_\{n \times m\}$-algebras is described and a characterization of $mLM_\{n \times m\}$-congruences in terms of special subsets of the associated space is shown. Moreover, the subsets which correspond to principal congruences are determined. Finally, some functional representation theorems for these algebras are given and the relationship between them is pointed out.},
author = {Figallo, A. V., Sanza, Claudia A.},
journal = {Mathematica Bohemica},
keywords = {$n$-valued Łukasiewicz-Moisil algebra; monadic $n$-valued Łukasiewicz-Moisil algebra; congruence; subdirectly irreducible algebra; discriminator variety; Priestley space; -valued Łukasiewicz-Moisil algebras; monadic -valued Łukasiewicz-Moisil algebras},
language = {eng},
number = {4},
pages = {425-447},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Monadic $n\times m$-valued Łukasiewicz-Moisil algebras},
url = {http://eudml.org/doc/246958},
volume = {137},
year = {2012},
}

TY - JOUR
AU - Figallo, A. V.
AU - Sanza, Claudia A.
TI - Monadic $n\times m$-valued Łukasiewicz-Moisil algebras
JO - Mathematica Bohemica
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 137
IS - 4
SP - 425
EP - 447
AB - Here we initiate an investigation into the class $mLM_{n\times m}$ of monadic $n\times m$-valued Łukasiewicz-Moisil algebras (or $mLM_{n \times m}$-algebras), namely $n\times m$-valued Łukasiewicz-Moisil algebras endowed with a unary operation. These algebras constitute a generalization of monadic $n$-valued Łukasiewicz-Moisil algebras. In this article, the congruences on these algebras are determined and subdirectly irreducible algebras are characterized. From this last result it is proved that $mLM_{n\times m}$ is a discriminator variety and as a consequence, the principal congruences are characterized. Furthermore, the number of congruences of finite $mLM_{n \times m}$-algebras is computed. In addition, a topological duality for $mLM_{n \times m}$-algebras is described and a characterization of $mLM_{n \times m}$-congruences in terms of special subsets of the associated space is shown. Moreover, the subsets which correspond to principal congruences are determined. Finally, some functional representation theorems for these algebras are given and the relationship between them is pointed out.
LA - eng
KW - $n$-valued Łukasiewicz-Moisil algebra; monadic $n$-valued Łukasiewicz-Moisil algebra; congruence; subdirectly irreducible algebra; discriminator variety; Priestley space; -valued Łukasiewicz-Moisil algebras; monadic -valued Łukasiewicz-Moisil algebras
UR - http://eudml.org/doc/246958
ER -

References

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