IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS

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