Completions of Noetherian P.I. rings

Amiram Braun

doi:10.1016/0021-8693(90)90273-Q

Completions of Noetherian P.I. rings

Amiram Braun

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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;lim_i 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 language	English
Pages (from-to)	340-350
Number of pages	11
Journal	Journal of Algebra
Volume	133
Issue number	2
DOIs	https://doi.org/10.1016/0021-8693(90)90273-Q
State	Published - Sep 1990

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/0021-8693(90)90273-Q

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title = "Completions of Noetherian P.I. rings",

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AB - 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 ̂).

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Completions of Noetherian P.I. rings

Abstract

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