| Title:
|
Ideals of noncommutative $DR\ell$-monoids (English) |
| Author:
|
Kühr, Jan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
97-111 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we introduce the concept of an ideal of a noncommutative dually residuated lattice ordered monoid and we show that congruence relations and certain ideals are in a one-to-one correspondence. (English) |
| Keyword:
|
dually residuated lattice ordered monoid |
| Keyword:
|
ideal |
| Keyword:
|
normal ideal |
| MSC:
|
06D35 |
| MSC:
|
06F05 |
| idZBL:
|
Zbl 1081.06017 |
| idMR:
|
MR2121658 |
| . |
| Date available:
|
2009-09-24T11:21:08Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127961 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] A. Dvurečenskij: Pseudo $MV$-algebras are intervals in $\ell $-groups.J. Austral. Math. Soc. 72 (2002), 427–445. MR 1902211, 10.1017/S1446788700036806 |
| 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.PhD. Thesis, Palacký Univ. Olomouc, 1996. |
| Reference:
|
[9] J. Rachůnek: Prime ideals in autometrized algebras.Czechoslovak Math. J. 112 (1987), 65–69. MR 0875128 |
| Reference:
|
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| Reference:
|
[11] K. L. N. Swamy: Dually residuated lattice ordered semigroups I.Math. Ann. 159 (1965), 105–114. MR 0183797, 10.1007/BF01360284 |
| Reference:
|
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| . |
