Localization, completion and the AR property in Noetherian P.I. rings

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Given a prime ideal P in a noetherian ring R we examine the following two properties: (1) P is Ore localizable. (2) The completion of R at P 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 ideal P in R to satisfy (1), where R is the enveloping algebra of complex solvable finite dimensional Lie algebra.

Original languageEnglish
Pages (from-to)115-140
Number of pages26
JournalIsrael Journal of Mathematics
StatePublished - 1996

ASJC Scopus subject areas

  • General Mathematics


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