Hollow and Semihollow Modules

Volume 19 , Issue 2 , June 2017 , Pages 203-220

Authors

Payman Mahmood Hama Ali 1 ; Basil A. Al-Hashimi 2

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

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

DOI logo 10.17656/jzs.10624

Keywords

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.

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  • Published at20 June 2017

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