Two questions on scalar-reflexive rings

Author:

Snashall Nicole

Abstract

A module M M over a commutative ring R R with unity is reflexive if the only R R -endomorphisms of M M leaving invariant every submodule of M M are the scalar multiplications by elements of R R . A commutative ring R R is scalar-reflexive if every finitely generated R R -module is reflexive. A local version of scalar-reflexivity is introduced, and it is shown that every locally scalar-reflexive ring is scalar-reflexive. An example is given of a scalar-reflexive domain that is not h h -local. This answers a question posed by Hadwin and Kerr. Theorem 7 gives eight equivalent conditions on an h h -local domain for it to be scalar-reflexive, thus classifying the scalar-reflexive h h -local domains.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference9 articles.

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