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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Failure of cancellation for direct sums of line bundles


Author: Richard G. Swan
Journal: Trans. Amer. Math. Soc. 336 (1993), 581-605
MSC: Primary 55N15; Secondary 13D15, 19A13
DOI: https://doi.org/10.1090/S0002-9947-1993-1091709-9
MathSciNet review: 1091709
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Abstract: In answer to a question of Murthy and Wiegand, examples are given of finitely generated projective modules $ L$ of rank $ 1$ over a commutative ring $ R$ such that $ L \oplus {L^{ - 1}}$ is stably free but not free.

Examples are also given of projective modules for which the determinant map det: $ \operatorname{Aut}(P) \to {R^{\ast} }$ is not onto. Some related topological questions are also discussed.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1091709-9
Article copyright: © Copyright 1993 American Mathematical Society