Scalar-reflexive rings

Hadwin, Don; Kerr, Jeanne Wald

doi:10.1090/S0002-9939-1988-0938634-2

Scalar-reflexive rings
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by Don Hadwin and Jeanne Wald Kerr PDF

Proc. Amer. Math. Soc. 103 (1988), 1-8 Request permission

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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