Abstract
We consider the group GL n A of all invertible n by n matrices over a ring A satisfying the first Bass stable range condition. We prove that every matrix is similar to the product of a lower and upper triangular matrix, and that it is also the product of two matrices each similar to a companion matrix. We use this to show that, when n ⩾3 and A is commutative, every matrix in SL n A is the product of two commutators.
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