J. Korean Math. Soc. 2016; 53(2): 447-459
Printed March 1, 2016
https://doi.org/10.4134/JKMS.2016.53.2.447
Copyright © The Korean Mathematical Society.
Gyu Whan Chang
Incheon National University
Let $D$ be an integral domain, $\{X_{\alpha}\}$ be a nonempty set of indeterminates over $D$, and ${D[\![\{X_{\alpha}\}]\!]_1}$ be the first type power series ring over $D$. We show that if $D$ is a $t$-SFT Pr\"ufer $v$-multiplication domain, then ${D[\![\{X_{\alpha}\}]\!]_1}_{D - \{0\}}$ is a Krull domain, and $D[\![\{X_{\alpha}\}]\!]_1$ is a Pr\"ufer $v$-multiplication domain if and only if $D$ is a Krull domain.
Keywords: $t$-operation, $t$-SFT P$v$MD, power series ring, Krull domain
MSC numbers: 13A15, 13F05, 13F25
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