| Title:
|
New operations on partial Abelian monoids defined by preideals (English) |
| Author:
|
Vinceková, Elena |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
44 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
441-450 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider partial abelian monoids, in particular generalized effect algebras. From the given structures, we construct new ones by introducing a new operation $\oplus $, which is given by restriction of the original partial operation + with respect to a special subset called preideal. We bring some derived properties and characterizations of these new built structures, supporting the results by illustrative examples. (English) |
| Keyword:
|
partial abelian monoid |
| Keyword:
|
generalized effect algebra |
| Keyword:
|
preideal |
| Keyword:
|
Riesz decomposition property |
| Keyword:
|
central element |
| MSC:
|
08A55 |
| MSC:
|
81P10 |
| idZBL:
|
Zbl 1154.81305 |
| idMR:
|
MR2436043 |
| . |
| Date available:
|
2009-09-24T20:36:20Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135862 |
| . |
| Reference:
|
[1] Dvurečenskij A., Pulmannová S.: New Trends in Quantum Structures.Kluwer Academic Publishers, Dordrecht 2000 MR 1861369 |
| Reference:
|
[2] Foulis D. J., Bennett M. K.: Effect algebras and unsharp quantum logics.Found. Phys. 24 (1994), 1325–1346 MR 1304942 |
| Reference:
|
[3] Hedlíková J., Pulmannová S.: Generalized difference posets and orthoalgebras.Acta Math. Univ. Comenian. 45 (1996), 247–279 Zbl 0922.06002, MR 1451174 |
| Reference:
|
[4] Pulmannová S., Vinceková E.: Riesz ideals in generalized effect algebras and in their unitizations.Algebra Universalis 57 (2007), 4, 393–417 Zbl 1139.81007, MR 2373250 |
| Reference:
|
[5] Riečanová Z., Marinová I.: Generalized homogeneous, prelattice and MV-effect algebras.Kybernetika 41 (2005), 2, 129–142 MR 2138764 |
| . |
