| Title:
|
Congruences and ideals in lattice effect algebras as basic algebras (English) |
| Author:
|
Pulmannová, Silvia |
| Author:
|
Vinceková, Elena |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
45 |
| Issue:
|
6 |
| Year:
|
2009 |
| Pages:
|
1030-1039 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found. (English) |
| Keyword:
|
basic algebra |
| Keyword:
|
effect algebra |
| Keyword:
|
ideal |
| Keyword:
|
congruence |
| MSC:
|
03G12 |
| MSC:
|
06C15 |
| MSC:
|
08A55 |
| MSC:
|
81P10 |
| idZBL:
|
Zbl 1200.62055 |
| idMR:
|
MR2650081 |
| . |
| Date available:
|
2010-06-02T19:33:47Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140021 |
| . |
| Reference:
|
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| Reference:
|
[2] I. Chajda, R. Halaš, and J. Kühr: Many valued quantum algebras.Alg. Univ. 60 (2009), 63–90. MR 2480632 |
| Reference:
|
[3] C. C. Chang: Algebraic analysis of many valued logics.Trans. Amer. Math. Soc. 88 (1958), 467–490. Zbl 0084.00704, MR 0094302 |
| Reference:
|
[4] F. Chovanec and F. Kôpka: Boolean D-posets.Tatra Mt. Math. Publ. 10 (1997), 1–15. MR 1469294 |
| Reference:
|
[5] A. Dvurečenskij and S. Pulmannová: New Trends in Quantum Structures.Kluwer Academic Publishers, Dordrecht 2000. MR 1861369 |
| Reference:
|
[6] D. Foulis and M. K. Bennett: Effect algebras and unsharp quantum logics.Found. Phys. 24 (1994), 1331–1352. MR 1304942 |
| Reference:
|
[7] R. Giuntini: Quantum MV-algebras.Studia Logica 56 (1996), 303–417. Zbl 1093.06011, MR 1397488 |
| Reference:
|
[8] S. Gudder: Total extensions of effect algebras.Found. Phys. Lett. 8 (1995), 243–252. MR 1339403 |
| Reference:
|
[9] G. Jenča and S. Pulmannová: Ideals and quotients in lattice ordered effect albebras.Soft Computing 5 (2001), 376–380. |
| Reference:
|
[10] F. Kôpka and F. Chovanec: D-posets.Math. Slovaca 44 (1994), 21–34. MR 1290269 |
| . |
