Completions of Noetherian P.I. rings

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Let R be a left noetherian p.i. ring and M a maximal (semimaximal) ideal in R satisfying ∩iMi = {0}. It is proven that R ̂&z.tbnd;limi R Mi, the completion of R with respect to {Mi}, is left noetherian, settling affirmatively a conjecture of Goldie [G]. However, usually R ̂ is neither left nor right flat over R and height (M) ≠ height( M ̂).

Original languageEnglish
Pages (from-to)340-350
Number of pages11
JournalJournal of Algebra
Issue number2
StatePublished - Sep 1990

ASJC Scopus subject areas

  • Algebra and Number Theory


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