Pawar, Y. S.; Dhamke, V. B. 0-distributive posets. (English) Zbl 0676.06009 Indian J. Pure Appl. Math. 20, No. 8, 804-811 (1989). 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. Cited in 1 Document MSC: 06A06 Partial orders, general Keywords:0-distributive poset; annihilator ideals; Boolean algebra × Cite Format Result Cite Review PDF