Chatters, A. W., Hajarnavis, C. R. and Lissaman, R. M. (2001) Projective prime ideals and localisation in pi-rings. Journal of the London Mathematical Society, Vol.64 (No.1). pp. 1-12. doi:10.1017/S0024610701002125

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Abstract

The results here generalise [2, Proposition 4.3] and [9, Theorem 5.11]. We shall prove the following.

THEOREM A. Let R be a Noetherian PI-ring. Let P be a non-idempotent prime ideal of R such that PR is projective. Then P is left localisable and RP is a prime principal left and right ideal ring.

We also have the following theorem.

THEOREM B. Let R be a Noetherian PI-ring. Let M be a non-idempotent maximal ideal of R such that MR is projective. Then M has the left AR-property and M contains a right regular element of R.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Algebra, Homological, Associative rings, Associative algebras
Journal or Publication Title:	Journal of the London Mathematical Society
Publisher:	Cambridge University Press
ISSN:	0024-6107
Official Date:	August 2001
Dates:	Date Event August 2001 Published
Volume:	Vol.64
Number:	No.1
Page Range:	pp. 1-12
DOI:	10.1017/S0024610701002125
Status:	Peer Reviewed
Access rights to Published version:	Open Access
Funder:	London Mathematical Society (LMS)

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