ieja International Electronic Journal of Algebra 1306-6048 Abdullah HARMANCI 10.24330/ieja.440192 Mathematical Sciences Matematik IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS Christensen Katie Gipson Ryan Kulosman Hamid 07 05 2018 24 24 50 61 10 11 2017 Copyright © 2007, International Electronic Journal of Algebra 2007 International Electronic Journal of Algebra

We extend a lemma by Matsuda about the irreducibility of thebinomial X 􀀀 1 in the semigroup ring F[X;G], where F is a eld, G is anabelian 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 mainresult.

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