On Primarily Hollow Module - Jabbar, Adil Kadir; Hamaali, Payman Mahmood (Sulaimani Journal for Pure and Applied Sciences, 2018)
An R- module M is called primarily hollow module if every primary submodule of is a small submodule in. This definition extends several notions in the literature of hollow module. Some certain equivalent conditions to primarily hollow modules. Also, we verified that a primarily hollow module which contains a maximal submodule is a multiplication module and every multiplication primarily hollow module is indecomposable.
Keywords: Primary submodule; primarily hollow module; multiplication modulesubmodule