Word length in elementary matrices (Q1178855)

Let \(R\) be an associative ring with 1, \(E(n, R)\) the group generated by all elementary matrices, \( e_ n(R) \) the least \(s\) such that every element of \(E(n, R)\) is a product of \(s\) elementary matrices. Dennis and Vaserstein obtained some bounds for \( e_ n(R) \) for rings of finite stable rank in the case when \( e_ n(R) \) is finite for some \(n\). The author obtains other bounds involving other numbers instead of the stable rank.