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0-distributive posets. (English) Zbl 0676.06009

Summary: 0-distributivity in a partially ordered set (poset) is defined, and some equivalent formulations for 0-distributivity are obtained. It is shown that the notion of 0-distributive poset is a generalization of those of pseudocomplemented poset. Mainly, we prove the following: Theorem. For a 0-distributive poset P, the set of all annihilator ideals, A(P), is a Boolean algebra.

MSC:

06A06 Partial orders, general
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