## Rocky Mountain Journal of Mathematics

### Content formulas for power series and Krull domains

#### 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, $c(f/g)=c(f)c(g)^{-1}$.

#### Article information

Source
Rocky Mountain J. Math., Volume 46, Number 6 (2016), 2077-2088.

Dates
First available in Project Euclid: 4 January 2017

https://projecteuclid.org/euclid.rmjm/1483520439

Digital Object Identifier
doi:10.1216/RMJ-2016-46-6-2077

Mathematical Reviews number (MathSciNet)
MR3591273

Zentralblatt MATH identifier
1362.13005

#### Citation

Yin, Huayu; Chen, Youhua; Zhu, Xiaosheng. Content formulas for power series and Krull domains. Rocky Mountain J. Math. 46 (2016), no. 6, 2077--2088. doi:10.1216/RMJ-2016-46-6-2077. https://projecteuclid.org/euclid.rmjm/1483520439

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