a1 Mathematics Institute, University of Warwick, Coventry CV4 7AL, England
In general, a prime ideal P of a prime Noetherian ring need not be classically localisable. Since such a localisation, when it does exist, is a striking property; sufficiency criteria which guarantee it are worthy of careful study. One such condition which ensures localisation is when P is an invertible ideal [5, Theorem 1.3]. The known proofs of this result utilise both the left as well as the right invertiblity of P. Such a requirement is, in practice, somewhat restrictive. There are many occasions such as when a product of prime ideals is invertible  or when a non-idempotent maximal ideal is known to be projective only on one side , when the assumptions lead to invertibilty also on just one side. Our main purpose here is to show that in the context of Noetherian prime polynomial identity rings, this one-sided assumption is enough to ensure classical localisation [Theorem 3.5]. Consequently, if a maximal ideal in such a ring is invertible on one side then it is invertible on both sides [Proposition 4.1]. This result plays a crucial role in . As a further application we show that for polynomial identity rings the definition of a unique factorisation ring is left-right symmetric [Theorem 4.4].
(Received April 26 1991)