jzs-10738

On Primarily Hollow Module

 Adil Kadir Jabbar1 & Payman Mahmood Hamaali2

1 Mathematics Department, College of Science, University of Sulaimani, Kurdistan Region, Iraq

Original: 17 June 2017, Revised: 1 August 2018, Accepted: 12 September 2018, Published online: 20 December 2018

DOI Link: https://doi.org/10.17656/jzs.10738

Abstract

An R- module  M is called primarily hollow module if every primary submodule of  is a small submodule in. This definition extends several notions in the literature of hollow module. Some certain equivalent conditions to primarily hollow modules. Also, we verified that a primarily hollow module which contains a maximal submodule is a multiplication module and every multiplication primarily hollow module is indecomposable.

Key Words: Primary submodule, primarily hollow module, multiplication module(submodule)

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