Completion of skew completable unimodular rows

TL;DR

This paper proves that skew completable unimodular rows of odd length can be completed over polynomial extensions of local rings when the ring's dimension matches the row length.

Contribution

It establishes a new condition under which skew completable unimodular rows are completable over polynomial extensions of local rings.

Findings

Completable unimodular rows of odd length are achievable under specified conditions.

The result links the dimension of the local ring with the length of the unimodular row.

Provides a criterion for completion over polynomial extensions.

Abstract

Skew completable unimodular rows of odd length are completable over polynomial extension of a local ring if dimension of local ring and length of unimodular rows are same.