| Title:
|
Remarks on special ideals in lattices (English) |
| Author:
|
Beran, Ladislav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
4 |
| Year:
|
1994 |
| Pages:
|
607-615 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The author studies some characteristic properties of semiprime ideals. The semiprimeness is also used to characterize distributive and modular lattices. Prime ideals are described as the meet-irreducible semiprime ideals. In relatively complemented lattices they are characterized as the maximal semiprime ideals. $D$-radicals of ideals are introduced and investigated. In particular, the prime radicals are determined by means of $\hat C$-radicals. In addition, a necessary and sufficient condition for the equality of prime radicals is obtained. (English) |
| Keyword:
|
semiprime ideal |
| Keyword:
|
prime ideal |
| Keyword:
|
congruence of a lattice |
| Keyword:
|
allele |
| Keyword:
|
lattice polynomial |
| Keyword:
|
meet-irreducible element |
| Keyword:
|
kernel |
| Keyword:
|
forbidden exterior quotients |
| Keyword:
|
$D$-radical |
| Keyword:
|
prime radical |
| MSC:
|
06B10 |
| idZBL:
|
Zbl 0812.06002 |
| idMR:
|
MR1321231 |
| . |
| Date available:
|
2009-01-08T18:13:45Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118702 |
| . |
| Reference:
|
[1] Beran L.: Orthomodular Lattices (Algebraic Approach).Reidel Dordrecht (1985). Zbl 0558.06008, MR 0784029 |
| Reference:
|
[2] Beran L.: Distributivity in finitely generated orthomodular lattices.Comment. Math. Univ. Carolinae 28 (1987), 433-435. Zbl 0624.06008, MR 0912572 |
| Reference:
|
[3] Beran L.: On semiprime ideals in lattices.J. Pure Appl. Algebra 64 (1990), 223-227. Zbl 0703.06003, MR 1061299 |
| Reference:
|
[4] Beran L.: On the rhomboidal heredity in ideal lattices.Comment. Math. Univ. Carolinae 33 (1992), 723-726. Zbl 0782.06007, MR 1240194 |
| Reference:
|
[5] Birkhoff G.: Lattice Theory.3rd ed., American Math. Soc. Colloq. Publ., vol. XXV, Providence, 1967. Zbl 0537.06001, MR 0227053 |
| Reference:
|
[6] Chevalier G.: Semiprime ideals in orthomodular lattices.Comment. Math. Univ. Carolinae 29 (1988), 379-386. Zbl 0655.06008, MR 0957406 |
| Reference:
|
[7] Dubreil-Jacotin M.L., Lesieur L., Croisot R.: Leçons sur la théorie des treillis, des structures algébriques ordonnées et des treillis géometriques.Gauthier-Villars Paris (1953). Zbl 0051.26005, MR 0057838 |
| Reference:
|
[8] Rav Y.: Semiprime ideals in general lattices.J. Pure Appl. Algebra 56 (1989), 105-118. Zbl 0665.06006, MR 0979666 |
| . |
