✦ LIBER ✦
Functions on Distributive Lattices with the Congruence Substitution Property: Some Problems of Grätzer from 1964
✍ Scribed by Jonathan David Farley
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 305 KB
- Volume
- 149
- Category
- Article
- ISSN
- 0001-8708
No coin nor oath required. For personal study only.
✦ Synopsis
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 are characterized in terms of their Priestley spaces of prime ideals. For bounded distributive lattices L and M, it is shown that S 1 (L)$S 1 (M) implies S k (L)$S k (M). If L and M are finite, then S k (L)$S k (M) implies L$M. Some problems of Gra tzer dating to 1964 are thus solved.