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PROJECTIVE PRIME IDEALS AND LOCALISATION IN PI-RINGS

Published online by Cambridge University Press:  24 August 2001

A. W. CHATTERS ,
C. R. HAJARNAVIS  and
R. M. LISSAMAN
A. W. CHATTERS
Affiliation:
School of Mathematics, University Walk, Bristol BS8 1TW
C. R. HAJARNAVIS
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL
R. M. LISSAMAN
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL
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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 PRis projective. Then P is left localisable and RPis 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 MRis projective. Then M has the left AR-property and M contains a right regular element of R.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 1 - 12
Copyright
The London Mathematical Society 2001

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