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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Maximal ideal transforms of Noetherian rings

Author: Jacob R. Matijevic
Journal: Proc. Amer. Math. Soc. 54 (1976), 49-52
MathSciNet review: 0387269
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Abstract: Let $ R$ be a commutative Noetherian ring with unit. Let $ T$ be the set of all elements of the total quotient ring of $ R$ whose conductor to $ R$ contains a power of a finite product of maximal ideals of $ R$. If $ A$ is any ring such that $ R \subset A \subset T$, then $ A/xA$ is a finite $ R$ module for any non-zero-divisor $ x$ in $ R$. It follows that if, in addition, $ R$ has no nonzero nilpotent elements, then any ring $ A$ such that $ R \subset A \subset T$ is Noetherian.

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Keywords: Conductor, ideal transform, global transform, Krull dimension, Krull-Akizuki theorem, Noetherian ring, Artinian module
Article copyright: © Copyright 1976 American Mathematical Society

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