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