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Some types of implicative ideals. (English) Zbl 0938.06004

The paper studies basic properties for five special types of implicative ideals (modular, pentagonal, even, rectangular and medial) – these five classes play an interesting role in the theory of Boolean algebras. In particular, the author concentrates on a complete description of all possible inclusion relations between the corresponding classes. He also exhibits examples showing that the considered concepts define different classes. As a by-product he obtains new characterizations of modularity and distributivity.

MSC:

06B10 Lattice ideals, congruence relations
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