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PROJECTIVE PRIME IDEALS AND LOCALISATION IN PI-RINGS

  • A. W. CHATTERS (a1), C. R. HAJARNAVIS (a2) and R. M. LISSAMAN (a2)

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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PROJECTIVE PRIME IDEALS AND LOCALISATION IN PI-RINGS

  • A. W. CHATTERS (a1), C. R. HAJARNAVIS (a2) and R. M. LISSAMAN (a2)

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