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Some types of implicative ideals

Ladislav Beran — 1998

Commentationes Mathematicae Universitatis Carolinae

This paper studies basic properties for five special types of implicative ideals (modular, pentagonal, even, rectangular and medial). The results are used to prove characterizations of modularity and distributivity.

On the rhomboidal heredity in ideal lattices

Ladislav Beran — 1992

Commentationes Mathematicae Universitatis Carolinae

We show that the class of principal ideals and the class of semiprime ideals are rhomboidal hereditary in the class of modular lattices. Similar results are presented for the class of ideals with forbidden exterior quotients and for the class of prime ideals.

Remarks on special ideals in lattices

Ladislav Beran — 1994

Commentationes Mathematicae Universitatis Carolinae

The author studies some characteristic properties of semiprime ideals. The semiprimeness is also used to characterize distributive and modular lattices. Prime ideals are described as the meet-irreducible semiprime ideals. In relatively complemented lattices they are characterized as the maximal semiprime ideals. D -radicals of ideals are introduced and investigated. In particular, the prime radicals are determined by means of C ^ -radicals. In addition, a necessary and sufficient condition for the equality...

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