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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.
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참고문헌 (19)
참고문헌 신청
D. D. Anderson / 1998 / Anti-Archimedean rings and power series rings / Comm. Algebra 26:3223~3238
D. D. Anderson / 1991 / Almost Bezout domains / J. Algebra 142:285~309
J. Arnold / 1973 / Power series rings over Pr¨ufer domains / Pacific J. Math 44:1~11
J. Arnold / 1982 / Power series rings with finite Krull dimension / Indiana Univ. Math. J 31:897~911
G. W. Chang / 2002 / A pinched-Krull domain at a prime ideal / Comm. Algebra 30:3669~3686
D. D. Anderson / 1991 / Almost Bezout domains / J. Algebra 142:285~309
J. Arnold / 1973 / Power series rings over Pr¨ufer domains / Pacific J. Math 44:1~11
J. Arnold / 1982 / Power series rings with finite Krull dimension / Indiana Univ. Math. J 31:897~911
G. W. Chang / 2002 / A pinched-Krull domain at a prime ideal / Comm. Algebra 30:3669~3686
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