| Title:
|
Atoms in lattice of radical classes of lattice-ordered groups (English) |
| Author:
|
Ton, Dao-Rong |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
29 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
221-226 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
There are several special kinds of radical classes. For example, a product radical class is closed under forming product, a closed-kernel radical class is closed under taking order closures, a $K$-radical class is closed under taking $K$-isomorphic images, a polar kernel radical class is closed under taking double polars, etc. The set of all radical classes of the same kind is a complete lattice. In this paper we discuss atoms in these lattices. We prove that every nontrivial element in these lattices has a cover. (English) |
| Keyword:
|
lattice-ordered group |
| Keyword:
|
radical class |
| Keyword:
|
closure operator |
| Keyword:
|
atom |
| MSC:
|
06F15 |
| idZBL:
|
Zbl 0801.06031 |
| idMR:
|
MR1263123 |
| . |
| Date available:
|
2008-06-06T21:25:01Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107484 |
| . |
| Reference:
|
[1] Anderson, M., Feil, T.: Lattice-Ordered Groups (An Introduction).D. Reidel Publishing Company, 1988. MR 0937703 |
| Reference:
|
[2] Bleier, R. D., Conrad, P.: $a^*$-closures of lattice-ordered groups.Trans. Math. Soc. 209 (1975), 367-387. MR 0404087 |
| Reference:
|
[3] Conrad, P.: Lattice-Ordered Groups.Tulane Lecture Notes (1970), Tulane University. Zbl 0258.06011 |
| Reference:
|
[4] Conrad, P.: $K$-radical classes of lattice ordered groups.Algebra, Proc. Conf. Carbondale (1980), Lecture Notes Math., 848, 186-207. MR 0613186 |
| Reference:
|
[5] Darnel, M.: Closure operators on radical classes of lattice-ordered groups.Czech. Math. J. 37(112) (1987), 51-64. Zbl 0661.06007, MR 0875127 |
| Reference:
|
[6] Glass, A. M. W., Holland, W. C.: Lattice-Ordered Groups (Advances and Techniques).Kluwer Academic Publisher, 1989. MR 1036072 |
| Reference:
|
[7] Jakubik, J.: Radical mappings and radical classes of lattice ordered groups.Symposia Math. 21 (1977), 451-477, Academic Press. Zbl 0368.06013, MR 0491397 |
| Reference:
|
[8] Jakubik, J.: On $K$-radical classes of lattice ordered groups.Czech. Math. J. 33(108) (1983), 149-163. Zbl 0521.06016, MR 0687428 |
| Reference:
|
[9] Kenny, G. O.: Lattice-Ordered Groups.Ph.D. dissertation, University of Kansas (1975). MR 2625950 |
| Reference:
|
[10] Martinez, J.: Torsion theory for lattice ordered groups.Czech. Math. J. 25(100) (1975), 284-299. Zbl 0321.06020, MR 0389705 |
| Reference:
|
[11] Ton, Dao-Rong: Product radical classes of $\ell $-groups.Czech. Math. J. 42(117) (1992), 129-142. MR 1152176 |
| . |
