Extendibility criterion for a projective module of rank one over $R[T]$ and $R[T,T^ {-1}]$
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- by S. M. Bhatwadekar and P. L. N. Varma PDF
- Proc. Amer. Math. Soc. 119 (1993), 1069-1075 Request permission
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
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N. Bourbaki, Commutative algebra, Addison-Wesley, Reading, MA, 1972.
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 1069-1075
- MSC: Primary 13C10; Secondary 13F20
- DOI: https://doi.org/10.1090/S0002-9939-1993-1156463-6
- MathSciNet review: 1156463