Pawar, Y. S. 0-1 distributive lattices. (English) Zbl 0765.06015 Indian J. Pure Appl. Math. 24, No. 3, 173-179 (1993). A lattice \(L\) with 0 is called 0-distributive if \(a\wedge b=0\) and \(a\wedge c=0\) imply \(a\wedge(b\vee c)=0\). The definition of a 1- distributive lattice is similar. If \(L\) is 0-distributive and 1- distributive then it is called 0-1 distributive. The author gives different characterizations of complemented 0-1 distributive lattices in terms of maximal ideals. A bounded, 0-distributive, weakly complemented lattice in which every prime ideal is maximal is a Boolean lattice. Reviewer: E.T.Schmidt (Budapest) Cited in 1 Document MSC: 06D99 Distributive lattices 06B99 Lattices Keywords:0-distributive lattice; 1-distributive lattice; 0–1 distributive lattices; maximal ideals; complemented lattice; prime ideal; Boolean lattice × Cite Format Result Cite Review PDF