A change of rings result for Matlis reflexivity
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- by Douglas J. Dailey and Thomas Marley PDF
- Proc. Amer. Math. Soc. 145 (2017), 1837-1841 Request permission
Abstract:
Let $R$ be a commutative Noetherian ring and $E$ the minimal injective cogenerator of the category of $R$-modules. An $R$-module $M$ is (Matlis) reflexive if the natural evaluation map $M{\longrightarrow }\mathrm {Hom}_R(\mathrm {Hom}_R(M,E),E)$ is an isomorphism. We prove that if $S$ is a multiplicatively closed subset of $R$ and $M$ is an $R_S$-module which is reflexive as an $R$-module, then $M$ is a reflexive $R_S$-module. The converse holds when $S$ is the complement of the union of finitely many nonminimal primes of $R$, but fails in general.References
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Additional Information
- Douglas J. Dailey
- Affiliation: Department of Mathematics, University of Dallas, Irving, Texas 75062-4736
- Email: ddailey@udallas.edu
- Thomas Marley
- Affiliation: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588-0130
- MR Author ID: 263869
- Email: tmarley1@unl.edu
- Received by editor(s): October 14, 2015
- Received by editor(s) in revised form: May 11, 2016
- Published electronically: January 26, 2017
- Additional Notes: The first author was partially supported by U.S. Department of Education grant P00A120068 (GAANN)
- Communicated by: Irena Peeva
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1837-1841
- MSC (2010): Primary 13C05; Secondary 13C13
- DOI: https://doi.org/10.1090/proc/13287
- MathSciNet review: 3611300