Absolute stable rank and quadratic forms over noncommutative rings, K-Theory 4

A~tract. Given an associative ring A, let asr(A) denote the absolute stable range of A, as defined in [5]. We prove that asr(A) ~< 1 + Kdim A if A is a right Noetherian ring, and that asr(A) ~< 1 + cl-Kdim A if A is an afline PI algebra. Combined with results from [5], this provides a cancellation theorem ('Witt cancellation') for quadratic spaces defined over such a ring A. Key words. Absolute stable rank, Witt cancellation, quadratic spaces, Noetherian rings, aflhae H rings. O