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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 affine PI algebra. Combined with results from [5], this provides a cancellation theorem ('Witt cancellation') for quadratic spaces defined over such a ring A

Absolute stable rank and quadratic forms over noncommutative rings