IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS

Abstract

We extend a lemma by Matsuda about the irreducibility of the binomial X 􀀀 1 in the semigroup ring F[X;G], where F is a eld, G is an abelian torsion-free group and is an element of G of height (0; 0; 0; : : : ). In our extension, G is replaced by any submonoid of (Q+; +). The eld F, however, has to be of characteristic 0. We give an application of our main result.