IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS

被引：2
|
作者：
Christensen, Katie [1 ]
Gipson, Ryan [1 ]
Kulosman, Hamid [1 ]
机构：
[1] Univ Louisville, Dept Math, South 3rd St, Louisville, KY 40292 USA
来源：
INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA | 2018年 / 24卷
关键词：
Semigroup ring; atomic domain; AP domain; irreducible element; prime element; height (0,0,0,...);
D O I：
10.24330/ieja.440192
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We extend a lemma by Matsuda about the irreducibility of the binomial X-pi - 1 in the semigroup ring F [X; G], where F is a field, G is an abelian torsion-free group and pi 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.
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页码：50 / 61
页数：12
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