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The Kernels of Skeletal Congruences on a Distributive Lattice

✍ Scribed by William H. Cornish


Publisher
John Wiley and Sons
Year
1978
Tongue
English
Weight
648 KB
Volume
84
Category
Article
ISSN
0025-584X

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πŸ“œ SIMILAR VOLUMES


The rank of a distributive lattice
✍ I. Rabinovitch; I. Rival πŸ“‚ Article πŸ“… 1979 πŸ› Elsevier Science 🌐 English βš– 427 KB

The rank of a partial ordering P is the maximum size of an n-redundant family of linear extensions of P whose intersection is P. A simple relationship is established between the rank of a finite distributive lattice and its subset of join irreducible elements.

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Let L be a bounded distributive lattice. For k 1, let S k (L) be the lattice of k-ary functions on L with the congruence substitution property (Boolean functions); let S(L) be the lattice of all Boolean functions. The lattices that can arise as S k (L) or S(L) for some bounded distributive lattice L

Every Algebraic Chain Is the Congruence
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The equivalence of the following conditions on a chain \(L\) is proved: (1) \(L\) is algebraic; (2) There is a right chain domain \(T\) (with identity) such that \(L\) is isomorphic to the chain of proper two-sided ideals of \(T\) and all two-sided ideals of \(T\) are idempotent; (3) \(L\) is isomor

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✍ W.F. Doran IV πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 167 KB

This paper gives a method for computing the reduced poset homology of the rank-selected subposet of a distributive lattice. As an example of the method, let L be the lattice S b acts on L by permuting coordinates. For S βŠ† [ab], we give a description of the decomposition of the reduced homology of L