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

 

About direct summands of projective modules over Laurent polynomial rings


Author: Satya Mandal
Journal: Proc. Amer. Math. Soc. 112 (1991), 915-918
MSC: Primary 13C10; Secondary 13B25
MathSciNet review: 1069691
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Abstract: Suppose $ A$ is a local ring and $ R = A[X,{X^{ - 1}}]$ is a Laurent polynomial ring. We prove that for projective $ R$-modules $ P$ and $ Q$ with rank $ Q < $ rank $ P$ , if $ {Q_f}$ is a direct summand of $ {P_f}$ for a doubly monic polynomial $ f$ then $ Q$ is also a direct summand of $ P$. We also prove the analogue of the Horrock's theorem for Laurent polynomials rings.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1069691-3
PII: S 0002-9939(1991)1069691-3
Article copyright: © Copyright 1991 American Mathematical Society