| Title:
|
Banaschewski’s theorem for generalized $MV$-algebras (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
1099-1105 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A generalized $MV$-algebra $\mathcal A$ is called representable if it is a subdirect product of linearly ordered generalized $MV$-algebras. Let $S$ be the system of all congruence relations $\rho $ on $\mathcal A$ such that the quotient algebra $\mathcal A/\rho $ is representable. In the present paper we prove that the system $S$ has a least element. (English) |
| Keyword:
|
generalized $MV$-algebra |
| Keyword:
|
representability |
| Keyword:
|
congruence relation |
| Keyword:
|
unital lattice ordered group |
| MSC:
|
06D35 |
| MSC:
|
06F15 |
| idZBL:
|
Zbl 1174.06318 |
| idMR:
|
MR2357582 |
| . |
| Date available:
|
2009-09-24T11:51:55Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128229 |
| . |
| Reference:
|
[1] B. Banaschewski: On lattice-ordered groups.Fund. Math. 55 (1964), 113–122. Zbl 0129.01803, MR 0168672, 10.4064/fm-55-2-113-122 |
| Reference:
|
[2] G. Birkhoff: Lattice Theory.Third Edition, Providence, 1967. Zbl 0153.02501, MR 0227053 |
| Reference:
|
[3] P. Conrad: Lattice Ordered Groups.Tulane University, 1970. Zbl 0258.06011 |
| Reference:
|
[4] A. Dvurečenskij,: Pseudo MV-algebras are intervals of $\ell $-groups.J. Austral. Math. Soc. 72 (2002), 427–445. MR 1902211, 10.1017/S1446788700036806 |
| Reference:
|
[5] A. Dvurečenskij, S. Pulmannová: New Trends in Quantum Structures.Kluwer Academic Publishers, Dordrecht, 2000. MR 1861369 |
| Reference:
|
[6] G. Georgescu, A. Iorgulescu: Pseudo $MV$-algebras: a noncommutative extension of $MV$-algebras.In: The Proceedings of the Fourth International Symposium on Economic Informatics, INFOREC, Bucharest, 6–9 May, Romania, 1999, pp. 961–968. MR 1730100 |
| Reference:
|
[7] G. Georgescu, A. Iorgulescu: Pseudo $MV$-algebras.Multiple-Valued Logic 6 (2001), 95–135. MR 1817439 |
| Reference:
|
[8] J. Jakubík: Normal prime filters of a lattice ordered group.Czech. Math. J. 24 (1974), 91–96. MR 0347702 |
| Reference:
|
[9] J. Jakubík: Subdirect product decompositions of MV-algebras.Czech. Math. J. 49 (1999), 163–173. MR 1676813, 10.1023/A:1022472528113 |
| Reference:
|
[10] J. Rachůnek: A non-commutative generalization of $MV$-algebras.Czech. Math. J. 52 (2002), 255–273. MR 1905434, 10.1023/A:1021766309509 |
| . |
