| Title:
|
On product $MV$-algebras (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
797-810 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we apply the notion of the product $MV$-algebra in accordance with the definition given by B. Riečan. We investigate the convex embeddability of an $MV$-algebra into a product $MV$-algebra. We found sufficient conditions under which any two direct product decompositions of a product $MV$-algebra have isomorphic refinements. (English) |
| Keyword:
|
$MV$-algebras |
| Keyword:
|
product |
| Keyword:
|
convex |
| Keyword:
|
embedding |
| Keyword:
|
direct |
| Keyword:
|
decomposition |
| MSC:
|
06D35 |
| idZBL:
|
Zbl 1012.06014 |
| idMR:
|
MR1940060 |
| . |
| Date available:
|
2009-09-24T10:56:51Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127765 |
| . |
| Reference:
|
[1] G. Cattaneo and F. Lombardo: Independent axiomatization for $MV$-algebras.Tatra Mt. Math. Publ. 15 (1998), 227–232. MR 1655091 |
| Reference:
|
[2] R. Cignoli, I. M. I. D’Ottaviano and D. Mundici: Algebraic Foundations of Many-Valued Reasoning.Kluwer Academic Publishers, Dordrecht, 2000. MR 1786097 |
| Reference:
|
[3] P. Conrad: Lattice Ordered Groups.Tulane University, 1971. Zbl 0235.06006 |
| Reference:
|
[4] A. Dvurečenskij and A. DiNola: Product $MV$-algebras.Multiple Valued Logic 6 (2001), 193–251. MR 1777248 |
| Reference:
|
[5] A. Dvurečenskij and B. Riečan: Weakly divisible $MV$-algebras and product.J. Math. Anal. Appl. 234 (1999), 208–222. MR 1694841, 10.1006/jmaa.1999.6353 |
| Reference:
|
[6] L. Fuchs: Partially Ordered Algebraic Systems.Pergamon Press, Oxford, 1964. MR 0218283 |
| Reference:
|
[7] D. Gluschankof: Cyclic ordered groups and $MV$-algebras.Czechoslovak Math. J. 43(118) (1993), 249–263. Zbl 0795.06015, MR 1211747 |
| Reference:
|
[8] J. Jakubík: Direct product decompositions of $MV$-algebras.Czechoslovak Math. J. 44(119) (1994), 725–739. MR 1295146 |
| Reference:
|
[9] J. Jakubík: On complete $MV$-algebras.Czechoslovak Math. J. 45(120) (1995), 473–480. MR 1344513 |
| Reference:
|
[10] D. Mundici: Interpretation of $AFC^*$-algebra in Łukasiewics sentential calculus.J. Funct. Anal. 65 (1986), 15–63. 10.1016/0022-1236(86)90015-7 |
| Reference:
|
[11] B. Riečan: On the product $MV$-algebras.Tatra Mt. Math. Publ. 16 (1999), 143–149. MR 1725292 |
| . |
