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Displaying similar documents to “Meanders in lattices.”

Balanced d-lattices are complemented

Martin Goldstern, Miroslav Ploščica (2002)

Discussiones Mathematicae - General Algebra and Applications

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We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.

Remarks on special ideals in lattices

Ladislav Beran (1994)

Commentationes Mathematicae Universitatis Carolinae

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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...