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Projective prime ideals and localisation in pi-rings

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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 ISSN 0024-6107.

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Official URL: http://dx.doi.org/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:
DateEvent
August 2001Published
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 (Creative Commons)
Funder: London Mathematical Society (LMS)

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