On F-Z-hollow and Z-semihollow modules

摘要

In this work, F-Z-hollow and Z-semihollow modules are defined as a generalization of F-hollow and semihollow modules, and some properties of these concepts of modules are investigated. Where an R-module E over a ring R is F-Z-hollow if every proper submodule of E is F-Z-small in E. And we say that a nonzero R-module E is Z-semihollow module if every proper finitely generated submodule of E Z-small submodule.