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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회지 대한수학회지 제58권 제6호
- 발행연도
- 2021.11
- 수록면
- 1,311 - 1,325 (15page)
- DOI
- 10.4134/JKMS.j200475
이용수
초록· 키워드
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One says that a ring homomorphism $R \rightarrow S$ is \emph{Ohm-Rush} if extension commutes with arbitrary intersection of ideals, or equivalently if for any element $f\in S$, there is a unique smallest ideal of $R$ whose extension to $S$ contains $f$, called the \emph{content} of $f$. For Noetherian local rings, we analyze whether the completion map is Ohm-Rush. We show that the answer is typically `yes' in dimension one, but `no' in higher dimension, and in any case it coincides with the content map having good algebraic properties. We then analyze the question of when the Ohm-Rush property globalizes in faithfully flat modules and algebras over a 1-dimensional Noetherian domain, culminating both in a positive result and a counterexample. Finally, we introduce a notion that we show is strictly between the Ohm-Rush property and the weak content algebra property.
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참고문헌 (18)
참고문헌 신청
N. Bourbaki / 1972 / Elements of mathematics. Commutative algebra / Hermann
R. Dedekind / 1892 / Uber einen arithmetischen Satz von Gauß, Mittheilungen der Deutschen Mathematischen Gesellschaft in Prag / Tempsky :1~11
Paul Eakin / 1972 / Rings Which are Almost Polynomial Rings / Transactions of the American Mathematical Society 174:425
N. Epstein / 2016 / A Dedekind-Mertens theorem for power series rings / Proc. Amer. Math. Soc 144(3):917~924
Neil Epstein / 2015 / The Ohm–Rush content function / Journal of Algebra and Its Applications 15(01):1650009
R. Dedekind / 1892 / Uber einen arithmetischen Satz von Gauß, Mittheilungen der Deutschen Mathematischen Gesellschaft in Prag / Tempsky :1~11
Paul Eakin / 1972 / Rings Which are Almost Polynomial Rings / Transactions of the American Mathematical Society 174:425
N. Epstein / 2016 / A Dedekind-Mertens theorem for power series rings / Proc. Amer. Math. Soc 144(3):917~924
Neil Epstein / 2015 / The Ohm–Rush content function / Journal of Algebra and Its Applications 15(01):1650009
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