Completion of skew completable unimodular rows

Abstract

In this paper, we prove that if R is a local ring of dimension \(d\ge 3\), d odd and \(\frac{1}{(d-1)!}\in R\) then any skew completable unimodular row \(v\in Um_{d}(R[X])\) is completable. It is also proved that skew completable unimodular rows of size \(d\ge 3\) over a regular local ring of dimension d are first row of a 2- stably elementary matrix.