Geodesic
One sided invertibility and localisation II
Glasgow mathematical journal, Tome 37 (1995) no. 1, pp. 15-19

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The aim of this paper is to generalise the results of [7] from the prime to the semiprime case. It was shown, for instance, that if M is the annihilator of a simple right module S of projective dimension 1 over a Noetherian prime polynomial identity (PI) ring R then M is either an invertible ideal or an idempotent ideal [7, Proposition 4.2]. One of the main applications of this result was that a prime Noetherian affine PI ring of global dimension less than or equal to 2 is a finite module over its centre. It turns out that this theorem is valid more generally when the ring is semiprime [1, Theorem A]. Clearly this requires [7, Proposition 4.2] also to be strengthened to the semiprime case. We do this by showing that a right invertible maximal ideal in a semiprime Noetherian PI ring is also left invertible (Theorem 3.5). 
Hajarnavis, C. R. One sided invertibility and localisation II. Glasgow mathematical journal, Tome 37 (1995) no. 1, pp. 15-19. doi: 10.1017/S0017089500030330
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