Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad
,IN
Keywords:
Polynomial Ring, Matrix, Unimodular Row.
Abstract
Let A be a ring and f1(X), · · · ,fn(X) be a unimodular row over A[X] with f1(X) monic. Then we can find a matrix which can be connected to the identity matrix taking the column (f1, · · · , fn)T to (1, 0, · · ·,0)T. In this paper we have given two elementary proofs of this result.