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Journal of the London Mathematical Society 2001 64(1):1-12; doi:10.1017/S0024610701002125
© 2001 by London Mathematical Society
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© The London Mathematical Society

Projective Prime Ideals and Localisation in PI-Rings

A. W. Chatters, C. R. Hajarnavis and R. M. Lissaman

School of Mathematics University Walk, Bristol BS8 1TW
Mathematics Institute, University of Warwick Coventry CV4 7AL

Received 20 December 1999. Revision received 12 September 2000.

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.


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