A representation theorem for tense -valued Łukasiewicz-Moisil algebras

Aldo Victorio Figallo; Gustavo Pelaitay

Mathematica Bohemica (2015)

  • Volume: 140, Issue: 3, page 345-360
  • ISSN: 0862-7959

Abstract

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In 2000, Figallo and Sanza introduced -valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of -valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class tLM of tense -valued Łukasiewicz-Moisil algebras (or tense LM-algebras), namely -valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense Łukasiewicz-Moisil algebras (or tense LM-algebras). Our most important result is a representation theorem for tense LM-algebras. Also, as a corollary of this theorem, we obtain the representation theorem given by Georgescu and Diaconescu in 2007, for tense LM-algebras.

How to cite

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Figallo, Aldo Victorio, and Pelaitay, Gustavo. "A representation theorem for tense $n\times m$-valued Łukasiewicz-Moisil algebras." Mathematica Bohemica 140.3 (2015): 345-360. <http://eudml.org/doc/271573>.

@article{Figallo2015,
abstract = {In 2000, Figallo and Sanza introduced $n\times m$-valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of $n$-valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class tLM$_\{n\times m\}$ of tense $n\times m$-valued Łukasiewicz-Moisil algebras (or tense LM$_\{n\times m\}$-algebras), namely $n\times m$-valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense Łukasiewicz-Moisil algebras (or tense LM$_\{n\}$-algebras). Our most important result is a representation theorem for tense LM$_\{n\times m\}$-algebras. Also, as a corollary of this theorem, we obtain the representation theorem given by Georgescu and Diaconescu in 2007, for tense LM$_\{n\}$-algebras.},
author = {Figallo, Aldo Victorio, Pelaitay, Gustavo},
journal = {Mathematica Bohemica},
keywords = {$n$-valued Łukasiewicz-Moisil algebra; tense $n$-valued Łukasiewicz-Moisil algebra; $n\times m$-valued Łukasiewicz-Moisil algebra},
language = {eng},
number = {3},
pages = {345-360},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A representation theorem for tense $n\times m$-valued Łukasiewicz-Moisil algebras},
url = {http://eudml.org/doc/271573},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Figallo, Aldo Victorio
AU - Pelaitay, Gustavo
TI - A representation theorem for tense $n\times m$-valued Łukasiewicz-Moisil algebras
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 3
SP - 345
EP - 360
AB - In 2000, Figallo and Sanza introduced $n\times m$-valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of $n$-valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class tLM$_{n\times m}$ of tense $n\times m$-valued Łukasiewicz-Moisil algebras (or tense LM$_{n\times m}$-algebras), namely $n\times m$-valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense Łukasiewicz-Moisil algebras (or tense LM$_{n}$-algebras). Our most important result is a representation theorem for tense LM$_{n\times m}$-algebras. Also, as a corollary of this theorem, we obtain the representation theorem given by Georgescu and Diaconescu in 2007, for tense LM$_{n}$-algebras.
LA - eng
KW - $n$-valued Łukasiewicz-Moisil algebra; tense $n$-valued Łukasiewicz-Moisil algebra; $n\times m$-valued Łukasiewicz-Moisil algebra
UR - http://eudml.org/doc/271573
ER -

References

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