| Title:
|
On ideals of lattice ordered monoids (English) |
| Author:
|
Jasem, Milan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
132 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
369-387 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper the notion of an ideal of a lattice ordered monoid $A$ is introduced and relations between ideals of $A$ and congruence relations on $A$ are investigated. Further, it is shown that the set of all ideals of a soft lattice ordered monoid or a negatively ordered monoid partially ordered by inclusion is an algebraic Brouwerian lattice. (English) |
| Keyword:
|
lattice ordered monoid |
| Keyword:
|
ideal |
| Keyword:
|
normal ideal |
| Keyword:
|
congruence relation |
| Keyword:
|
dually residuated lattice ordered monoid |
| MSC:
|
06F05 |
| idZBL:
|
Zbl 1174.06328 |
| idMR:
|
MR2365322 |
| DOI:
|
10.21136/MB.2007.133965 |
| . |
| Date available:
|
2009-09-24T22:32:45Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133965 |
| . |
| 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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| Reference:
|
[8] T. Kovář: A General Theory of Dually Residuated Lattice Ordered Monoids.Doctoral Thesis, Palacký Univ., Olomouc, 1996. |
| Reference:
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[9] J. Kühr: Dually Residuated Lattice Ordered Monoids.Doctoral Thesis, Palacký Univ., Olomouc, 2003. Zbl 1066.06008, MR 2070377 |
| Reference:
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[10] J. Kühr: Ideals of non-commutative DRl-monoids.Czech. Math. J. 55 (2005), 97–111. MR 2121658, 10.1007/s10587-005-0006-0 |
| Reference:
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[11] J. Kühr: Prime ideals and polars in DRl-monoids and pseudo BL-algebras.Math. Slovaca 53 (2003), 233–246. MR 2025020 |
| Reference:
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| Reference:
|
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| Reference:
|
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| . |
