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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Extendibility criterion for a projective module of rank one over $ R[T]$ and $ R[T,T\sp {-1}]$


Authors: S. M. Bhatwadekar and P. L. N. Varma
Journal: Proc. Amer. Math. Soc. 119 (1993), 1069-1075
MSC: Primary 13C10; Secondary 13F20
MathSciNet review: 1156463
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Abstract: In this note we give a criterion for a finitely generated projective module $ \mathcal{P}$ of constant rank one over $ R[T]$ or $ R[T,{T^{ - 1}}]$ 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^{ - 1}}]$ such that $ I \cap R \ne 0$, then $ I$ is extended from $ R$ if and only if $ I \cap R$ is an invertible ideal of $ R$.


References [Enhancements On Off] (What's this?)

  • [1] N. Bourbaki, Commutative algebra, Addison-Wesley, Reading, MA, 1972.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1156463-6
PII: S 0002-9939(1993)1156463-6
Article copyright: © Copyright 1993 American Mathematical Society