| Title:
|
Direct product decompositions of bounded commutative residuated $\ell$-monoids (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
1129-1143 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The notion of bounded commutative residuated $\ell $-monoid ($BCR$ $\ell $-monoid, in short) generalizes both the notions of $MV$-algebra and of $BL$-algebra. Let $\c A$ be a $BCR$ $\ell $-monoid; we denote by $\ell (\c A)$ the underlying lattice of $\c A$. In the present paper we show that each direct product decomposition of $\ell (\c A)$ determines a direct product decomposition of $\c A$. This yields that any two direct product decompositions of $\c A$ have isomorphic refinements. We consider also the relations between direct product decompositions of $\c A$ and states on $\c A$. (English) |
| Keyword:
|
bounded commutative residuated $\ell$-monoid |
| Keyword:
|
lattice |
| Keyword:
|
direct product decomposition |
| Keyword:
|
internal direct factor |
| MSC:
|
03G25 |
| MSC:
|
06D35 |
| MSC:
|
06F05 |
| idZBL:
|
Zbl 1174.06327 |
| idMR:
|
MR2471171 |
| . |
| Date available:
|
2010-07-21T08:12:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140445 |
| . |
| 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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| Reference:
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| Reference:
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| . |
