| Title:
|
Generalizations of pseudo MV-algebras and generalized pseudo effect algebras (English) |
| Author:
|
Kühr, Jan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
395-415 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We deal with unbounded dually residuated lattices that generalize pseudo $MV$-algebras in such a way that every principal order-ideal is a pseudo $MV$-algebra. We describe the connections of these generalized pseudo $MV$-algebras to generalized pseudo effect algebras, which allows us to represent every generalized pseudo $MV$-algebra $A$ by means of the positive cone of a suitable $\ell $-group $G_A$. We prove that the lattice of all (normal) ideals of $A$ and the lattice of all (normal) convex $\ell $-subgroups of $G_A$ are isomorphic. We also introduce the concept of Archimedeanness and show that every Archimedean generalized pseudo $MV$-algebra is commutative. (English) |
| Keyword:
|
pseudo $MV$-algebra |
| Keyword:
|
$DR\ell $-monoid |
| Keyword:
|
generalized pseudo effect algebra |
| MSC:
|
03G25 |
| MSC:
|
06F05 |
| idZBL:
|
Zbl 1174.06330 |
| idMR:
|
MR2411097 |
| . |
| Date available:
|
2009-09-24T11:55:34Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128265 |
| . |
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