| Title:
|
Direct product decompositions of pseudo $MV$-algebras (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
37 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
131-142 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we deal with the relations between the direct product decompositions of a pseudo $MV$-algebra and the direct product decomposicitons of its underlying lattice. (English) |
| Keyword:
|
pseudo $MV$-algebra |
| Keyword:
|
direct product decomposition |
| MSC:
|
03G25 |
| MSC:
|
06D35 |
| idZBL:
|
Zbl 1070.06003 |
| idMR:
|
MR1838410 |
| . |
| Date available:
|
2008-06-16T21:22:04Z |
| Last updated:
|
2014-10-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116920 |
| . |
| Reference:
|
[1] Chajda, I., Halaš, R. and Rachůnek, J.: Ideals and congruences in generalized $MV$-algebras.Demonstratio Math. (to appear). MR 1769414 |
| Reference:
|
[2] Cignoli, R., D’Ottaviano, M. I. and Mundici, D.: Algebraic Foundations of many-valued Reasoning, Trends in Logic, Studia Logica Library Vol. 7.Kluwer Academic Publishers, Dordrecht, 2000. MR 1786097, 10.1007/978-94-015-9480-6 |
| Reference:
|
[3] Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures.Kluwer Academic Publishers, Dordrecht-Boston-London and Ister Science, Bratislava, 2000. MR 1861369 |
| Reference:
|
[4] Dvurečenskij, A.: Pseudo $MV$-algebras are intervals in $\ell $-groups.J. Austral. Math. Soc. (to appear). |
| Reference:
|
[5] Georgescu, G., Iorgulescu, A.: Pseudo $MV$-algebras: a noncommutative extension of $MV$-algebras.In: The Proceedings of the Fourth International Symposium on Economic Informatics, Bucharest, 6–9 May, Romania, 1999, pp. 961–968. MR 1730100 |
| Reference:
|
[6] Georgescu, G., Iorgulescu, A.: Pseudo $MV$-algebras.Multiple-Valued Logic (a special issue dedicated to Gr. C. Moisil) 6 (2001), 95–135. MR 1817439 |
| Reference:
|
[7] Hashimoto, J.: On direct product decompositions of partially ordered sets.Annals of Math. 54 (1951), 315–318. MR 0043067, 10.2307/1969532 |
| Reference:
|
[8] Jakubík, J.: Direct products of $MV$-algebras.Czechoslovak Math. J. 44 (1994), 725–739. |
| Reference:
|
[9] Jakubík, J.: Convex chains in a pseudo $MV$-algebra.Czechoslovak Math. J. (to appear). MR 1962003 |
| Reference:
|
[10] Leustean, I.: Local pseudo $MV$-algebras.(submitted). Zbl 0992.06011 |
| Reference:
|
[11] Rachůnek, J.: A non-commutative generalization of $MV$-algebras.Czechoslovak Math. J. (to appear). MR 1905434 |
| Reference:
|
[12] Rachůnek, J.: Prime spectra of non-commutative generalizations of $MV$-algebras.(submitted). |
| . |
