ON COMPLETELY PRIME SUBMODULES

Year 2016, , 77 - 90, 01.06.2016

David Ssevviiri

https://doi.org/10.24330/ieja.266194

Abstract

The formal study of completely prime modules was initiated by
N. J. Groenewald and the current author in the paper: Completely prime
submodules, Int. Electron. J. Algebra, 13(2013), 1–14. In this paper, the study
of completely prime modules is continued. Firstly, the advantage completely
prime modules have over prime modules is highlighted and different situations
that lead to completely prime modules given. Later, emphasis is put on fully
completely prime modules (i.e., modules whose all submodules are completely
prime). For a fully completely prime left R-module M, if a, b ∈ R and m ∈ M,
then abm = bam, am = a km for all positive integers k, and either am = abm
or bm = abm. In the last section, two different torsion theories induced by the
completely prime radical are given.

Keywords

Domain, prime module, completely prime module, completely prime radical, torsion theory