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초록· 키워드
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Let D be an integral domain, and let D be the integral closure of D. We show that if D is an almost pseudo-valuation domain (APVD), then D is a quasi-PrÄufer domain if and only if D/P is a quasi-PrÄufer domain for each prime ideal P of D, if and only if D is a valuation domain. We also show that D(X), the Nagata ring of D, is a locally APVD if and only if D is a locally APVD and D is a PrÄufer domain.
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참고문헌 (12)
참고문헌 신청
A. Badawi / 2002 / Powerful ideals, strongly primary ideals, almost pseudo-valuation domains, and conductive domains / Comm. Algebra 30 : 1591 ~ 1606
D. E. Dobbs / 1978 / Coherence, ascent of going-down, and pseudo-valuation domains / Houston J. Math. 4 : 551 ~ 567
D. E. Dobbs / 1983 / Locally pseudo-valuation domains / Ann. Mat. Pura Appl.(4) 134 : 147 ~ 168
E. Bastida / 1973 / Overrings and divisorial ideals of the form D + M / Michigan Math. J. 20 : 79 ~ 95
G. W. Chang / 2005 / Strongly primary ideals, in Arithmetical Properties of Commutative Rings and Monoids / Lecture Notes in Pure and Appl. Math. 241 : 378 ~ 386
D. E. Dobbs / 1978 / Coherence, ascent of going-down, and pseudo-valuation domains / Houston J. Math. 4 : 551 ~ 567
D. E. Dobbs / 1983 / Locally pseudo-valuation domains / Ann. Mat. Pura Appl.(4) 134 : 147 ~ 168
E. Bastida / 1973 / Overrings and divisorial ideals of the form D + M / Michigan Math. J. 20 : 79 ~ 95
G. W. Chang / 2005 / Strongly primary ideals, in Arithmetical Properties of Commutative Rings and Monoids / Lecture Notes in Pure and Appl. Math. 241 : 378 ~ 386
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