Distributive lattices, affine semigroup rings and algebras with straightening laws. (English) Zbl 0654.13015

Hibi, Takayuki

Commutative algebra and combinatorics, US-Jap. joint Semin., Kyoto/Jap. 1985, Adv. Stud. Pure Math. 11, 93-109 (1987).

[For the entire collection see Zbl 0632.00003.]
A lattice L is called integral over a field k if there exists a homogeneous ASL \((=algebra\) with straightening laws) domain on L over k. Using the fundamental theorem of Birkhoff, the author proves that every finite distributive lattice is integral in the above sense.

Reviewer: T.S.Blyth

MSC:

13C13	Other special types of modules and ideals in commutative rings
13F20	Polynomial rings and ideals; rings of integer-valued polynomials
06D99	Distributive lattices
20M25	Semigroup rings, multiplicative semigroups of rings

Keywords:

integral lattice; algebra with straightening laws; distributive lattice