Factorization by elementary matrices, null-homotopy and products of exponentials for invertible matrices over rings

Evgueni Doubtsov, Frank Kutzschebauch

Let $R$ be a commutative unital ring. A well-known factorization problem is whether any matrix in ${\mathrm{SL}}_n(R)$ is a product of elementary matrices with entries in $R$. To sol…