Strongly -regular rings have stable range one

A ring is said to be strongly -regular if for every there exist a positive integer and such that . For example, all algebraic algebras over a field are strongly -regular. We prove that every strongly -regular ring has stable range one. The stable range one condition is especially interesting because of Evans' Theorem, which states that a module cancels from direct sums whenever has stable range one. As a consequence of our main result and Evans' Theorem, modules satisfying Fitting's Lemma cancel from direct sums.