Hermite semigroup rings
Leo G. Chouinard · Pacific Journal of Mathematics · 1982
If S is a commutative, separative semigroup with identity, and R is a commutative ring with unit such that R[S] is arithmetical, then a local-global principle for verifying algebraic equations in R[S] is established.This is then used to show that if S is not a union of torsion groups, then R[S] is an elementary divisor ring.