MATHEMATICA BOHEMICA, Vol. 121, No. 2, pp. 117-120, 1996

A characterization of finite Stone pseudocomplemented ordered sets

Radomir Halas

Radomir Halas, Dept. of algebra and geometry, Fac. of Sci. UP Olomouc, Tomkova 40, 771 46 Olomouc, Czech Republic

Abstract: 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 $S$.

Keywords: distributive pseudocomplemented ordered set, Stone ordered set, prime ideal, $l$-ideal

Classification (MSC91): 06A99

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