Projective prime ideals and localisation in pi-rings
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. ISSN 0024-6107
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Official URL: http://dx.doi.org/10.1017/S0024610701002125
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 > 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|
|Official Date:||August 2001|
|Page Range:||pp. 1-12|
|Access rights to Published version:||Open Access|
|Funder:||London Mathematical Society (LMS)|
1. A. Braun, `Localization, completion and the AR-property in Noetherian PI-rings ', Israel J. Math. 96 (1996) 115±140.
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