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2016 Content formulas for power series and Krull domains
Huayu Yin, Youhua Chen, Xiaosheng Zhu
Rocky Mountain J. Math. 46(6): 2077-2088 (2016). DOI: 10.1216/RMJ-2016-46-6-2077

Abstract

Let $R$ be an integral domain with quotient field $K$, and let $X$ be an indeterminate over $R$. In this paper, we consider content formulae for power series in terms of $*$-operations for PVMDs, Krull domains and Dedekind domains, where $*$ is the star-operation, $d$, $w$, $t$, or $v$. We prove that $R$ is a Krull domain if and only if $c(f/g)_w=(c(f)c(g)^{-1})_w$ for all $f,g\in R[[X]]^*$ with $c(f/g)$ a fractional ideal if and only if $c(f/g)_t=(c(f)c(g)^{-1})_t$ for all $f,g\in R[[X]]^*$ with $c(f/g)$ a fractional ideal, and $R$ is a Dedekind domain if and only if for all $f,g\in R[[X]]^*$ with $c(f/g)$ a fractional ideal, $c(f/g)=c(f)c(g)^{-1}$.

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Huayu Yin. Youhua Chen. Xiaosheng Zhu. "Content formulas for power series and Krull domains." Rocky Mountain J. Math. 46 (6) 2077 - 2088, 2016. https://doi.org/10.1216/RMJ-2016-46-6-2077

Information

Published: 2016
First available in Project Euclid: 4 January 2017

zbMATH: 1362.13005
MathSciNet: MR3591273
Digital Object Identifier: 10.1216/RMJ-2016-46-6-2077

Subjects:
Primary: 13A15
Secondary: 13F05, 13F25

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

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Vol.46 • No. 6 • 2016
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