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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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
• ISSN: 0021-8693