Journal of the Ramanujan Mathematical Society

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On a Question of Roitman


Affiliations
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, India
     

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We show in this paper that if A is a commutative noetherian ring of finite Krull dimension n containing an infinite field and P is a projective A[T] -module of rank n such that Pf (T) has a unimodular element for some monic polynomial f(T) ∈ A[T], then P has a unimodular element.

Keywords

Projective Modules, Monic Polynomials, Unimodular Elements.
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  • On a Question of Roitman

Abstract Views: 310  |  PDF Views: 0

Authors

S. M. Bhatwadekar
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, India
Raja Sridharan
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, India

Abstract


We show in this paper that if A is a commutative noetherian ring of finite Krull dimension n containing an infinite field and P is a projective A[T] -module of rank n such that Pf (T) has a unimodular element for some monic polynomial f(T) ∈ A[T], then P has a unimodular element.

Keywords


Projective Modules, Monic Polynomials, Unimodular Elements.