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

 

Scalar-reflexive rings


Authors: Don Hadwin and Jeanne Wald Kerr
Journal: Proc. Amer. Math. Soc. 103 (1988), 1-8
MSC: Primary 13C13; Secondary 13E10
MathSciNet review: 938634
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Abstract: A module over a commutative ring is scalar-reflexive if the only endormorphisms that leave invariant every submodule are scalars. We investigate the class of rings for which every module is scalar-reflexive and the class of rings for which every finitely generated module is scalar-reflexive. For a certain class of rings we show that these properties are equivalent to every finitely generated module being a direct sum of cyclic modules.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0938634-2
PII: S 0002-9939(1988)0938634-2
Article copyright: © Copyright 1988 American Mathematical Society