POWER SERIES RINGS OVER PRÜFER v-MULTIPLICATION DOMAINS

Title & Authors
POWER SERIES RINGS OVER PRÜFER v-MULTIPLICATION DOMAINS
Chang, Gyu Whan;

Abstract
Let D be an integral domain, {$\small{X_{\alpha}}$} be a nonempty set of indeterminates over D, and $\small{D{\mathbb{[}}\{X_{\alpha}\}{\mathbb{}$$\small{]}$$\small{}_1}}$ be the first type power series ring over D. We show that if D is a t-SFT $\small{Pr{\ddot{u}}fer}$ v-multiplication domain, then $\small{D{\mathbb{[}}\{X_{\alpha}\}{\mathbb{}$$\small{]}$$\small{}}_{1_{D-\{0\}}}}$ is a Krull domain, and $\small{D{\mathbb{[}}\{X_{\alpha}\}{\mathbb{}$$\small{]}$$\small{}}_1}$ is a $\small{Pr{\ddot{u}}fer}$ v-multiplication domain if and only if D is a Krull domain.
Keywords
t-operation;t-SFT PvMD;power series ring;Krull domain;
Language
English
Cited by
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