| Title:
|
Modal Pseudocomplemented De Morgan Algebras (English) |
| Author:
|
Figallo, Aldo V. |
| Author:
|
Oliva, Nora |
| Author:
|
Ziliani, Alicia |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
65-79 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
pseudocomplemented De Morgan algebras |
| Keyword:
|
Priestley spaces |
| Keyword:
|
discriminator varieties |
| Keyword:
|
congruences |
| MSC:
|
03G99 |
| MSC:
|
06D15 |
| MSC:
|
06D30 |
| idZBL:
|
Zbl 06416942 |
| idMR:
|
MR3331071 |
| . |
| Date available:
|
2014-09-01T08:06:11Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143916 |
| . |
| Reference:
|
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