| Title:
|
Maximal completion of a pseudo MV-algebra (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
141-161 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper we investigate the relations between maximal completions of lattice ordered groups and maximal completions of pseudo $MV$-algebras. (English) |
| Keyword:
|
pseudo $MV$-algebra |
| Keyword:
|
maximal completion |
| Keyword:
|
$b$-atomicity |
| Keyword:
|
directproduct |
| MSC:
|
06B23 |
| MSC:
|
06D35 |
| MSC:
|
06F15 |
| idZBL:
|
Zbl 1108.06006 |
| idMR:
|
MR1994570 |
| . |
| Date available:
|
2008-06-06T22:41:31Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107860 |
| . |
| Reference:
|
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| Reference:
|
[2] Cignoli, R., D’Ottaviano, M. I., Mundici, D.: Algebraic Foundations of many-valued Reasoning.Trends in Logic, Studia Logica Library Vol. 7, Kluwer Academic Publishers, Dordrecht, 2000. MR 1786097 |
| Reference:
|
[3] Conrad, P.: Lattice Ordered Groups.Tulane University, 1970. Zbl 0258.06011 |
| Reference:
|
[4] Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum structures.Kluwer Academic Publishers, Dordrecht-Boston-London, and Ister Science, Bratislava, 2000. MR 1861369 |
| Reference:
|
[5] Dvurečenskij, A.: Pseudo $MV$-algebras are intervals in $\ell $-groups.J. Austral. Math. Soc. (to appear). |
| Reference:
|
[6] Everett, C. J.: Sequence completion of lattice modules.Duke Math. J. 11 (1994), 109–119. MR 0009592 |
| Reference:
|
[7] Fuchs, L.: Paritally Ordered Algebraic Systems.Pergamon Press, Oxford-New York-London-Paris, 1963. MR 0171864 |
| Reference:
|
[8] Georgescu, G., Iorgulescu, A.: Pseudo $MV$-algebras: a noncommutative extension of $MV$--algebras.The Proceedings of the Fourth International Symposium on Economic Informatics, Romania, 1999, pp. 961–968. MR 1730100 |
| Reference:
|
[9] Georgescu, G., Iorgulescu, A.: Pseudo $MV$-algebras.Multiple Valued Logic (a special issue dedicated to Gr. Moisil) vol. 6, 2001, pp. 95–135. MR 1817439 |
| Reference:
|
[10] Jakubík, J.: Maximal Dedekind completion of an abelian lattice ordered group.Czechoslovak Math. J. 28 (1978), 611–631. MR 0506435 |
| Reference:
|
[11] Jakubík,J.: Direct product decompositions of $MV$-algebras.Czechoslovak Math. J. 44 (1994), 725–739. |
| Reference:
|
[12] Jakubík, J.: Complete generators and maximal completions of $MV$-algebras.Czechoslovak Math. J. 48 (1998), 597–608. MR 1637863 |
| Reference:
|
[13] Jakubík, J.: Basic elements in a pseudo $MV$-algebra.Soft Computing (to appear). MR 1901010 |
| Reference:
|
[14] Jakubík, J.: Direct product decompositions of pseudo $MV$-algebras.Archivum Math. (to appear). MR 1838410 |
| Reference:
|
[15] Jakubík, J.: Strong subdirect products of $MV$-algebras.(Submitted). |
| Reference:
|
[16] Rachůnek, J.: A noncommutative generalization of $MV$-algebras.Czechoslovak Math. J. 25 (2002), 255–273. |
| . |
