Products of involutory matrices over rings Original Research Article

Let αεGLn A be a matrix over a commutative ring A with 1 such that (det α)2 = 1. If α is cyclic, it can be written as a product of at most three involutions. When A satisfies the first Bass stable range condition, then α can be written as a product of at most five involutions. If in addition either n less-than-or-equals, slant 3 or n = 4 and det α = −1, then α can be written as a product of at most four involutions. When A is a Dedekind ring of arithmetic type, the number of involutions needed to express α is uniformly bounded for any n greater-or-equal, slanted 3. When A = C[x] the number of involutions is unbounded for any n ≥ 2.