Nearly locally hollow modules

Document Type : Research Paper


Department of Mathematics, College of Education for Pure Science, University of Tikrit, Tikrit, Iraq


Let $R$ be a commutative ring with identity and let $M$ be an R-module. This study presents the nearly locally hollow module that's a strong form of a hollow module. We present that an $R$-module $M$ is nearly locally hollow if M has a unique semi-maximal sub-module that contains all small sub-modules of $M$. The current study deals with this class of modules and gives several fundamental properties related to this concept.