Generalised Mennicke-Newman lemma

TL;DR

This paper generalizes the Mennicke--Newman lemma from unimodular rows to right invertible matrices, expanding its applicability in algebraic K-theory.

Contribution

It extends the Mennicke--Newman lemma to m×n right invertible matrices, broadening its theoretical scope.

Findings

Generalized Mennicke--Newman lemma for matrices

Provides new algebraic tools for matrix analysis

Potential applications in algebraic K-theory

Abstract

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