| Title:
|
Dually residuated $\ell$-monoids having no non-trivial convex subalgebras (English) |
| Author:
|
Kühr, Jan |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
103-108 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we describe the structure of dually residuated $\ell $-monoids ($\mathit{DR}\ell $-monoids) that have no non-trivial convex subalgebras. (English) |
| Keyword:
|
$\mathit{DR}\ell $-monoid |
| Keyword:
|
$\mathit{GPMV}$-algebra |
| Keyword:
|
Archimedean property |
| MSC:
|
03G25 |
| MSC:
|
06F05 |
| idZBL:
|
Zbl 1125.06012 |
| idMR:
|
MR2321302 |
| . |
| Date available:
|
2009-08-21T07:03:52Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133438 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Georgescu G., Leuştean L., Preoteasa V.: Pseudo-hoops.. J. Mult.-Val. Log. Soft Comput. 11 (2005), 153–184. Zbl 1078.06007, MR 2162590 |
| Reference:
|
[4] Glass A. M. W.: Partially Ordered Groups. : World Scientific, Singapore., 1999. MR 1791008 |
| Reference:
|
[5] Jipsen P., Tsinakis C.: A survey of residuated lattices.. In: Ordered Algebraic Structures (Martinez, J., ed.), Kluwer Acad. Publ., Dordrecht, 2002, pp. 19–56. Zbl 1070.06005, MR 2083033 |
| Reference:
|
[6] Kovář T.: A General Theory of Dually Residuated Lattice Ordered Monoids. : Ph.D. thesis, Palacký University, Olomouc., 1996. |
| Reference:
|
[7] Kühr J.: Ideals of noncommutative $DR\ell $-monoids.Czechoslovak Math. J. 55 (2005), 97–111. MR 2121658 |
| Reference:
|
[8] Kühr J.: On a generalization of pseudo MV-algebras.J. Mult.-Val. Log. Soft Comput. (to appear). MR 2288689 |
| Reference:
|
[9] Kühr J.: Generalizations of pseudo MV-algebras and generalized pseudo effect algebras.Submitted. Zbl 1174.06330 |
| Reference:
|
[10] Swamy K. L. N.: Dually residuated lattice ordered semigroups.. Math. Ann. 159 (1965), 105–114. Zbl 0138.02104, MR 0183797 |
| . |
