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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Modules over the endomorphism ring of a finitely generated projective module


Author: F. L. Sandomierski
Journal: Proc. Amer. Math. Soc. 31 (1972), 27-31
DOI: https://doi.org/10.1090/S0002-9939-1972-0288137-4
MathSciNet review: 0288137
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Abstract: Let $ {P_R}$ be a projective module with trace ideal $ T$. An $ R$-module $ {X_R}$ is $ T$-accessible if $ XT = X.{\text{ If }}{P_R}$ is finitely generated projective and $ C$ is the $ R$-endomorphism ring of $ {P_R}$, such that $ _C{P_R}$, then for $ {X_R}$, Horn $ {({P_R},{X_R})_C}$ is artinian (noetherian) if and only if $ {X_R}$ satisfies the minimum (maximum) condition on $ T$-accessible submodules. Further, if $ {X_R}$ is $ T$-accessible then Hom $ {({P_R},{X_R})_C}$ is finitely generated if and only if $ {X_R}$ is finitely generated.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0288137-4
Keywords: Projective module, chain conditions
Article copyright: © Copyright 1972 American Mathematical Society