| Title:
|
On central atoms of Archimedean atomic lattice effect algebras (English) |
| Author:
|
Kalina, Martin |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
46 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
609-620 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
If element $z$ of a lattice effect algebra $(E,\oplus, {\mathbf 0}, {\mathbf 1})$ is central, then the interval $[{\mathbf 0},z]$ is a lattice effect algebra with the new top element $z$ and with inherited partial binary operation $\oplus$. It is a known fact that if the set $C(E)$ of central elements of $E$ is an atomic Boolean algebra and the supremum of all atoms of $C(E)$ in $E$ equals to the top element of $E$, then $E$ is isomorphic to a direct product of irreducible effect algebras ([16]). In [10] Paseka and Riečanová published as open problem whether $C(E)$ is a bifull sublattice of an Archimedean atomic lattice effect algebra $E$. We show that there exists a lattice effect algebra $(E,\oplus, {\mathbf 0}, {\mathbf 1})$ with atomic $C(E)$ which is not a bifull sublattice of $E$. Moreover, we show that also $B(E)$, the center of compatibility, may not be a bifull sublattice of $E$. (English) |
| Keyword:
|
lattice effect algebra |
| Keyword:
|
center |
| Keyword:
|
atom |
| Keyword:
|
bifullness |
| MSC:
|
03G12 |
| MSC:
|
03G27 |
| MSC:
|
06B99 |
| idZBL:
|
Zbl 1214.06002 |
| idMR:
|
MR2722091 |
| . |
| Date available:
|
2010-10-22T05:21:12Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140774 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
