Strongly FI-hollow-lifting modules

Abstract EN

In this paper, we introduce and study the concept of strongly FI-hollow-lifting modules.

As proper stronger concept of FI-hollow-lifting modules which is a proper generalization of strongly lifting modules.

We say that an R-module M called strongly FI- hollow-lifting module if every fully invariant submodule N of M with M/N is hollow there exists a fully invariant direct summand K of M such that K coessential submodule N in M.

Many characterizations and properties of strongly FI-hollow-lifting modules are given and the relation between this type of module and some other known of modules are discussed