| Title:
|
Convex chains in a pseudo MV-algebra (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
113-125 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a pseudo $MV$-algebra $\mathcal A$ we denote by $\ell (\mathcal A)$ the underlying lattice of $\mathcal A$. In the present paper we investigate the algebraic properties of maximal convex chains in $\ell (\mathcal A)$ containing the element 0. We generalize a result of Dvurečenskij and Pulmannová. (English) |
| Keyword:
|
pseudo $MV$-algebra |
| Keyword:
|
convex chain |
| Keyword:
|
Archimedean property |
| Keyword:
|
direct product decomposition |
| MSC:
|
06D35 |
| idZBL:
|
Zbl 1014.06010 |
| idMR:
|
MR1962003 |
| . |
| Date available:
|
2009-09-24T10:59:43Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127785 |
| . |
| 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] P. Conrad: Lattice Ordered Groups.Tulane University, 1970. Zbl 0258.06011 |
| Reference:
|
[3] A. Dvurečenskij and S. Pulmannová: New Trends in Quantum Structures.Kluwer Academic Publishers, Dordrecht, and Ister Science, Bratislava, 2000. MR 1861369 |
| Reference:
|
[4] G. Georgescu and A. Iorgulescu: Pseudo $MV$-algebras: a noncommutative extension of $MV$-algebras.In: The Proceedings of the Fourth International Symposyium on Economic Informatics, Bucharest, 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: Direct product of $MV$-algebras.Czechoslovak Math. J. 44(119) (1994), 725–739. MR 1295146 |
| Reference:
|
[7] J. Jakubík: Direct product decompositions of pseudo $MV$-algebras.Arch. Math. 37 (2001), 131–142. MR 1838410 |
| Reference:
|
[8] J. Jakubík: On chains in $MV$-algebras.Math. Slovaca 51 (2001), 151–166. MR 1841444 |
| Reference:
|
[9] J. Rachůnek: A non-commutative generalization of $MV$-algebras.Czechoslovak Math. J. 52(127) (2002), 255–273. MR 1905434, 10.1023/A:1021766309509 |
| . |
