The Journal of the Indian Mathematical Society

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On Completable Unimodular Row over a Polynomial Ring


Affiliations
1 Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad, India
     

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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.

Keywords

Polynomial Ring, Matrix, Unimodular Row.
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  • On Completable Unimodular Row over a Polynomial Ring

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Authors

Sumit Kumar Upadhyay
Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad, India

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.

Keywords


Polynomial Ring, Matrix, Unimodular Row.