IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS

Yıl 2018, Cilt: 24 Sayı: 24, 50 - 61, 05.07.2018

Katie Christensen Ryan Gipson Hamid Kulosman

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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