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Characterizations of 0-distributive posets. (English) Zbl 1112.06001

Summary: The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

MSC:

06A06 Partial orders, general
06C15 Complemented lattices, orthocomplemented lattices and posets
06D15 Pseudocomplemented lattices
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