Hollow and Semihollow Modules

Payman Mahmood Hama Ali & Basil A. Al-Hashimi

University of Sulaimani, College of Science, Department of Mathematics.

University of Baghdad, College of Science, Department of Mathematics.

DOI: https://doi.org/10.17656/jzs.10624

Original: 8 October 2016, Revised: 29 January 2017, Accepted: 22 February 2017, Published online: 20 June 2017

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.

Key Words: Hollow module, Semihollow Module, Small Submodules.

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