Ladislav Beran (1998)
Commentationes Mathematicae Universitatis Carolinae
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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.
Ladislav Beran (1992)
Commentationes Mathematicae Universitatis Carolinae
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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.
Ladislav Beran (1995)
Collectanea Mathematica
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Eva Bayer-Fluckiger (2000)
Journal de théorie des nombres de Bordeaux
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Several interesting lattices can be realised as over cyclotomic fields : some of the root lattices, the Coxeter-Todd lattice, the Leech lattice, etc. Many of these are in the sense of Quebbemann. The aim of the present paper is to determine the cyclotomic fields over which there exists a modular ideal lattice. We then study an especially simple class of lattices, the ideal lattices of . The paper gives a complete list of modular ideal lattices of trace type defined on cyclotomic fields. ...
M. Janowitz (1970)
Fundamenta Mathematicae
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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. -radicals of ideals are introduced and investigated. In particular, the prime radicals are determined by means of -radicals. In addition, a necessary and sufficient condition...