Injectivity relative to closed submodules |
| |
| Authors: | Engin Mermut Catarina Santa-Clara Patrick F Smith |
| |
| Institution: | 1. Dokuz Eylül Üniversitesi, Kaynaklar Yerle?kesi, Fen-Edebiyat Fakültesi, Matematik Bölümü, 35160 Buca/Izmir, Turkey;2. Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal;3. Centro de Álgebra da Universidade de Lisboa, Avenida Professor Gama Pinto, 2, 1649-003 Lisboa, Portugal;4. Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, UK |
| |
| 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. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
