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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:
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


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