Geodesic
A characterization of finite Stone pseudocomplemented ordered sets
Mathematica Bohemica, Tome 121 (1996) no. 2, pp. 117-120

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MR Zbl
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 $S$.
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 $S$.
DOI : 10.21136/MB.1996.126111
Classification : 06A99, 06D15
Keywords: Stone ordered set; prime ideal; distributive pseudocomplemented ordered set; $l$-ideal 
Halaš, Radomír. A characterization of finite Stone pseudocomplemented ordered sets. Mathematica Bohemica, Tome 121 (1996) no. 2, pp. 117-120. doi: 10.21136/MB.1996.126111
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