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2018 Weakly factorial property of a generalized Rees ring $D[X,d/X]$
Gyu Whan Chang
Rocky Mountain J. Math. 48(7): 2175-2185 (2018). DOI: 10.1216/RMJ-2018-48-7-2175

Abstract

Let $D$ be an integral domain, $X$ an indeterminate over $D$, $d \in D$, and $R = D[X, {d}/{X}]$ a subring of $D[X,{1}/{X}]$. In this paper, we show that $R$ is a weakly factorial domain if and only if $D$ is a weakly factorial GCD-domain and $d=0$, $d$ is a unit of $D$ or $d$ is a prime element of $D$. We also show that, if $D$ is a weakly factorial GCD-domain, $p$ is a prime element of $D$, and $n \geq 2$ is an integer, then $D[X, {p^n}/{X}]$ is an almost weakly factorial domain with $Cl(D[X, {p^n}/{X}]) = \mathbb {Z}_n$.

Citation

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Gyu Whan Chang. "Weakly factorial property of a generalized Rees ring $D[X,d/X]$." Rocky Mountain J. Math. 48 (7) 2175 - 2185, 2018. https://doi.org/10.1216/RMJ-2018-48-7-2175

Information

Published: 2018
First available in Project Euclid: 14 December 2018

zbMATH: 06999259
MathSciNet: MR3892129
Digital Object Identifier: 10.1216/RMJ-2018-48-7-2175

Subjects:
Primary: 13A15, 13F15

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 7 • 2018
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