| Title:
|
A representation theorem for tense $n\times m$-valued Łukasiewicz-Moisil algebras (English) |
| Author:
|
Figallo, Aldo Victorio |
| Author:
|
Pelaitay, Gustavo |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
140 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
345-360 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 {\bf 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. (English) |
| Keyword:
|
$n$-valued Łukasiewicz-Moisil algebra |
| Keyword:
|
tense $n$-valued Łukasiewicz-Moisil algebra |
| Keyword:
|
$n\times m$-valued Łukasiewicz-Moisil algebra |
| MSC:
|
03G20 |
| MSC:
|
06D30 |
| idZBL:
|
Zbl 06486944 |
| idMR:
|
MR3397262 |
| DOI:
|
10.21136/MB.2015.144400 |
| . |
| Date available:
|
2015-09-03T10:58:22Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144400 |
| . |
| Reference:
|
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| Reference:
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