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.
The Kernels of Skeletal Congruences on a Distributive Lattice
β Scribed by William H. Cornish
- Publisher
- John Wiley and Sons
- Year
- 1978
- Tongue
- English
- Weight
- 648 KB
- Volume
- 84
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
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
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 β [ab], we give a description of the decomposition of the reduced homology of L