| Title:
|
On varieties of pseudo $MV$-algebras (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
1031-1040 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we investigate the relation between the lattice of varieties of pseudo $MV$-algebras and the lattice of varieties of lattice ordered groups. (English) |
| Keyword:
|
pseudo $MV$-algebras |
| Keyword:
|
lattice ordered group |
| Keyword:
|
unital lattice ordered group |
| Keyword:
|
variety |
| MSC:
|
06D35 |
| MSC:
|
06F15 |
| MSC:
|
08B15 |
| idZBL:
|
Zbl 1080.06015 |
| idMR:
|
MR2018848 |
| . |
| Date available:
|
2009-09-24T11:08:57Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127858 |
| . |
| Reference:
|
[1] R. Cignoli, M. I. D’Ottaviano and D. Mundici: Algebraic Foundations of many-valued Reasoning.Trends in Logic, Studia Logica Library, Vol. 7, Kluwer Academic Publishers, Dordrecht, 2000. MR 1786097 |
| Reference:
|
[2] A. Dvurečenskij: Pseudo $MV$-algebras are intervals in $\ell $-groups.J. Austral. Math. Soc. (Ser. A) 72 (2002), 427–445. MR 1902211, 10.1017/S1446788700036806 |
| Reference:
|
[3] A. Dvurečenskij: States on pseudo $MV$-algebras.Studia Logica (to appear). MR 1865858 |
| Reference:
|
[4] G. Georgescu and A. Iorgulescu: Pseudo $MV$-algebras: a noncommutative extension of $MV$-algebras.In: The Proceedings of the Fourth International Symposium on Economic Informatics, Buchurest, Romania, 1999, pp. 961–968. MR 1730100 |
| Reference:
|
[5] G. Georgescu and A. Iorgulescu: Pseudo $MV$-algebras.Multiple-Valued Logic (a special issue dedicated to Gr. C. Moisil) 6 (2001), 95–135. MR 1817439 |
| Reference:
|
[6] J. Jakubík: Subdirect product decompositions of $MV$-algebras.Czechoslovak Math. J. 49 (1999), 163–173. MR 1676813, 10.1023/A:1022472528113 |
| Reference:
|
[7] J. Jakubík: Direct product decompositions of pseudo $MV$-algebras.Arch. Math. 37 (2001), 131–142. MR 1838410 |
| Reference:
|
[8] J. Rachůnek: A non-commutative generalization of $MV$-algebras.Czechoslovak Math. J. 52 (2002), 255–273. MR 1905434, 10.1023/A:1021766309509 |
| Reference:
|
[9] J. Rachůnek: Prime spectra of non-commutative generalizations of $MV$-algebras.(Submitted). |
| . |
