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Projective prime ideals and localisation in pirings
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Chatters, A. W., Hajarnavis, C. R. and Lissaman, R. M.. (2001) Projective prime ideals and localisation in pirings. Journal of the London Mathematical Society, Vol.64 (No.1). pp. 112. ISSN 00246107

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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 PIring. Let P be a nonidempotent 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 PIring. Let M be a nonidempotent maximal ideal of R such that MR is projective. Then M has the left ARproperty 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 
ISSN:  00246107 
Official Date:  August 2001 
Volume:  Vol.64 
Number:  No.1 
Page Range:  pp. 112 
Identification Number:  10.1017/S0024610701002125 
Status:  Peer Reviewed 
Access rights to Published version:  Open Access 
Funder:  London Mathematical Society (LMS) 
References:  1. A. Braun, `Localization, completion and the ARproperty in Noetherian PIrings ', Israel J. Math. 96 (1996) 115±140. 
URI:  http://wrap.warwick.ac.uk/id/eprint/805 
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