| Title:
|
A characterization of finite Stone pseudocomplemented ordered sets (English) |
| Author:
|
Halaš, Radomír |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
121 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
117-120 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A distributive pseudocomplemented set $S$ [2] is called Stone if for all $a\in S$ the condition $LU(a^*,a^{**})=S$ holds. It is shown that in a finite case $S$ is Stone iff the join of all distinct minimal prime ideals of $S$ is equal to $S$. (English) |
| Keyword:
|
Stone ordered set |
| Keyword:
|
prime ideal |
| Keyword:
|
distributive pseudocomplemented ordered set |
| Keyword:
|
$l$-ideal |
| MSC:
|
06A99 |
| MSC:
|
06D15 |
| idZBL:
|
Zbl 0863.06007 |
| idMR:
|
MR1400602 |
| DOI:
|
10.21136/MB.1996.126111 |
| . |
| Date available:
|
2009-09-24T21:16:56Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126111 |
| . |
| Reference:
|
[1] Grätzer G., Schmidt E. T.: On a problem of M.H. Stone.Acta Math. Sci. Hungarica 8 (1957), 455-460. MR 0092763, 10.1007/BF02020328 |
| Reference:
|
[2] Halaš R.: Pseudocomplemented ordered sets.Arch. Math. (Brno) 29 (1993), no. 3-4, 153-160. MR 1263116 |
| Reference:
|
[3] Halaš R.: Ideals, polars and annihilators in ordered sets.PҺD thesis, Olomouc, 1994. |
| Reference:
|
[4] Chajda I.: Complemented ordered sets.Aгch. Math. (Brno) 28 (1992), 25-34. Zbl 0785.06002, MR 1201863 |
| Reference:
|
[5] Chajda I., Rachůnek J.: Forbidden configurations for distributive and modular ordered sets.Order 5 (1989), 407-423. MR 1010389, 10.1007/BF00353659 |
| . |
