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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
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 | ||||
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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: |
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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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