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Semimodularity in lattices of congruences

✍ Scribed by Carl Eberhart; Wiley Williams

Publisher
Elsevier Science
Year
1978
Tongue
English
Weight
736 KB
Volume
52
Category
Article
ISSN
0021-8693

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πŸ“œ SIMILAR VOLUMES

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Faigle coined the notion of a strong lattice by singling out a property common to the join-irreducibles of a finite modular lattice and to the atoms of a geometric lattice. Many properties of both these classes of lattices carry over to strong semimodular lattices of finite length. Here we give a ne

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In this paper we prove that if -Y is a finite lattice, and r is an integral valued function on 2 satisfying some very natural conditions, then there exists a finite geometric (that is, semimodular and atomistic) lattice '/ containing 9 as a sublattice such that r is the height function of prestricte

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General theory of algebraic fuzzy systems developed earlier by the authors is applied to extend the Stone's prime ideal theorem to fuzzy ideals of distributive lattices. A correspondence between fuzzy ideals and fuzzy congruences in a distributive lattice is obtained and certain important properties