Injectivity relative to closed submodules

Mermut, E., Santaclara, C. and Smith, P. (2009) Injectivity relative to closed submodules. Journal of Algebra, 321(2), pp. 548-557. (doi: 10.1016/j.jalgebra.2008.11.004)

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Let R be a ring. An R-module X is called c-injective if, for every closed submodule L of every R-module M, every homomorphism from L to X lifts to M. It is proved that if R is a Dedekind domain then an R-module X is c-injective if and only if X is isomorphic to a direct product of homogeneous semisimple R-modules and injective R-modules. It is also proved that a commutative Noetherian domain R is Dedekind if and only if every simple R-module is c-injective.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Smith, Professor Patrick
Authors: Mermut, E., Santaclara, C., and Smith, P.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Algebra

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