| Title:
|
Some types of implicative ideals (English) |
| Author:
|
Beran, Ladislav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
1998 |
| Pages:
|
219-225 |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper studies basic properties for five special types of implicative ideals (modular, pentagonal, even, rectangular and medial). The results are used to prove characterizations of modularity and distributivity. (English) |
| Keyword:
|
implicative ideals |
| Keyword:
|
modular ideals |
| Keyword:
|
pentagonal ideals |
| Keyword:
|
even ideals |
| Keyword:
|
rectangular ideals |
| Keyword:
|
medial ideals |
| Keyword:
|
modularity |
| Keyword:
|
distributivity |
| MSC:
|
06B10 |
| MSC:
|
06C05 |
| MSC:
|
06C99 |
| MSC:
|
06D05 |
| MSC:
|
06D99 |
| idZBL:
|
Zbl 0938.06004 |
| idMR:
|
MR1651930 |
| . |
| Date available:
|
2009-01-08T18:40:14Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119001 |
| . |
| Reference:
|
[1] Beran L.: On semiprime ideals in lattices.Journ. Pure Appl. Algebra 64 (1990), 223-227. Zbl 0703.06003, MR 1061299 |
| Reference:
|
[2] Beran L.: Orthomodular Lattices (Algebraic Approach).Reidel Dordrecht (1985). Zbl 0558.06008, MR 0784029 |
| Reference:
|
[3] Beran L., Salvati S.: Boolean algebras revisited.Boll. Unione Matem. Italiana, ser. VII, 9 (sez. B) (1997), 895-901. Zbl 0895.06007, MR 1491733 |
| Reference:
|
[4] Rav Y.: Semiprime ideals in general lattices.Journ. Pure Appl. Algebra 56 (1989), 105-118. Zbl 0665.06006, MR 0979666 |
| Reference:
|
[5] Salvati S.: A characterization of Boolean algebras.Ricerche di Matematica 43 (1994), 357-363. Zbl 0915.06005, MR 1324757 |
| Reference:
|
[6] Zassenhaus H.: The Theory of Groups, (2nd ed.).Vandenhoeck & Ruprecht Göttingen (1958). Zbl 0083.24517, MR 0091275 |
| . |
