IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS

Year 2018, Volume: 24 Issue: 24, 50 - 61, 05.07.2018

Katie Christensen Ryan Gipson Hamid Kulosman

https://doi.org/10.24330/ieja.440192

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.

Keywords

Semigroup ring, atomic domain, AP domain, irreducible element, prime element

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