States Determinant Decomposition of K_1 for Commutative Rings: Let R be a commutative unital ring. For each n 1, let GL_n(R) be the group of invertible n n matrices over R, let GL(R)= _n GL_n(R) under the stabilization maps A diag(A,1_R), and let K_1(R) be the stable Whitehead group of R.