Hollow and Semihollow Modules

Abstract

Let be an associative ring with identity and be a non-zero unitary left module over . is called a hollow (semihollow) module if every proper (finitely generated proper) submodule of is a small submodule of . The purpose of this work is, to give a comprehensive study of hollow modules and semihollow modules. Moreover, we study the class of modules with finite spanning dimension. We supply the details of the proofs for almost all the results and we illustrate the concepts by examples. Also, we add some results that seem to be new to the best of our knowledge.