Generalised Mennicke-Newman lemma

Abstract

Mennicke--Newman lemma for unimodular rows was used by W. van der Kallen to give a group structure on the orbit set $\frac{U{m}_n(R)}{E_n(R)}$ for a commutative noetherian ring of dimension $d\le 2n-4.$ In this paper, we generalise the Mennicke--Newman lemma for $m\times n$ right invertible matrices.