f-Hollow modules

Abstract

In previous research, a concept was presented f –small submodules A submodule L of an R-module W is named f –small if L+X=W and W/X are small-singular, then X=W. In this work, we present a new concept, namely f –hollow modules, an R-module W is f-hollow if every submodule in W is an f-small submodule. This concept is an expansion of Hollow modules. Some characteristics are given in expansion to their relationship to a few of the concepts and the comparability between them is examined.