Bhatwadekar, S. M. ; Varma, P. L. N. (1993) Extendibility criterion for a projective module of rank one over R[T] and R[T,T_{1}] Proceedings of the American Mathematical Society, 119 (4). pp. 10691075. ISSN 00029939

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Official URL: http://www.ams.org/journals/proc/199311904/S0002...
Abstract
In this note we give a criterion for a finitely generated projective module P of constant rank one over R[ T ] or R[ T, T ] to be extended from R in terms of invertible ideals, when R is an integral domain. We show that if I is an invertible ideal of R[ T ] or R[ T, T ] such that I ∩ R ≠ 0, then I is extended from R if and only if I ∩ R is an invertible ideal of R.
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