Abstract
A module M over a ring is called simple-direct-injective if, whenever A and B are simple submodules of M with A≅B and B⊆⊕M, we have A⊆⊕M. Various basic properties of these modules are proved, and some well-studied rings are characterized using simple-direct-injective modules. For instance, it is proved that a ring R is artinian serial with Jacobson radical square zero if and only if every simple-direct-injective right R-module is a C3-module, and that a regular ring R is a right V-ring (i.e., every simple right R-module is injective) if and only if every cyclic right R-module is simple-direct-injective. The latter is a new answer to Fisher's question of when regular rings are V-rings [8].
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
