Localization,completion and the AR property in Noetherian P.I. rings |
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Authors: | Amiram Braun |
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Institution: | (1) Department of Mathematics, Haifa University, 31905 Haifa, Israel |
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Abstract: | Given a prime idealP in a noetherian ringR we examine the following two properties: (1)P is Ore localizable. (2) The completion ofR atP is Noetherian. For rings satisfying the 2nd layer condition a strong connection is discovered between (1) and (2) and consequently
questions by Goldie and McConnell are answered. As a corollary we also obtain a new characterization for non-maximal primitive
idealP inR to satisfy (1), whereR is the enveloping algebra of complex solvable finite dimensional Lie algebra
Dedicated to the memory of Shimshon Amitsur |
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Keywords: | |
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