| Title:
|
Remarks on ideals in lower-bounded dually residuated lattice-ordered monoids (English) |
| Author:
|
Kühr, Jan |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
105-112 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Lattice-ordered groups, as well as $GMV$-algebras (pseudo $MV$-algebras), are both particular cases of dually residuated lattice-ordered monoids ($DR\ell $-monoids for short). In the paper we study ideals of lower-bounded $DR\ell $-monoids including $GMV$-algebras. Especially, we deal with the connections between ideals of a $DR\ell $-monoid $A$ and ideals of the lattice reduct of $A$. (English) |
| Keyword:
|
$DR\ell $-monoid |
| Keyword:
|
ideal |
| Keyword:
|
prime ideal |
| MSC:
|
03G25 |
| MSC:
|
06F05 |
| idZBL:
|
Zbl 1071.06007 |
| idMR:
|
MR2124607 |
| . |
| Date available:
|
2009-08-21T12:54:35Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/132947 |
| . |
| Reference:
|
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| Reference:
|
[2] Georgescu G., Iorgulescu A.: Pseudo $MV$-algebras.Mult. Valued Log. 6 (2001), 95–135. Zbl 1014.06008, MR 1817439 |
| Reference:
|
[3] Kovář T.: A General Theory of Dually Residuated Lattice Ordered Monoids.Ph.D. Thesis, Palacký University, Olomouc, 1996. |
| Reference:
|
[4] Kühr J.: Ideals of noncommutative $DR\ell $-monoids.Czech. Math. J. (to appear). MR 2121658 |
| Reference:
|
[5] Kühr J.: Prime ideals and polars in $DR\ell $-monoids and pseudo $BL$-algebras.Math. Slovaca 53 (2003), 233–246. MR 2025020 |
| Reference:
|
[6] Kühr J.: A generalization of $GMV$-algebras.(submitted). |
| Reference:
|
[7] Rachůnek J.: $DR\ell $-semigroups and $MV$-algebras.Czech. Math. J. 48 (1998), 365–372. MR 1624268 |
| Reference:
|
[8] Rachůnek J.: $MV$-algebras are categorically equivalent to a class of $DR\ell _{1(i)}$-semigroups.Math. Bohem. 123 (1998), 437–441. MR 1667115 |
| Reference:
|
[9] Rachůnek J.: Connections between ideals of non-commutative generalizations of $MV$-algebras and ideals of their underlying lattices.Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 40 (2001), 195–200. Zbl 1040.06005, MR 1904695 |
| Reference:
|
[10] Rachůnek J.: A non-commutative generalization of $MV$-algebras.Czech. Math. J. 52 (2002), 255–273. Zbl 1012.06012 |
| Reference:
|
[11] Swamy K. L. N.: Dually residuated lattice ordered semigroups.Math. Ann. 159 (1965), 105–114. Zbl 0138.02104, MR 0183797 |
| . |
