Author:
CHATTERS A. W.,HAJARNAVIS C. R.,LISSAMAN R. M.
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.
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