Abstract
The purpose of this paper is to further study the concept of a very important module theory namely principally supplemented modules. Therefore, our work presents some properties of the relation between lifting property and principally supplemented module. Also we will focus on quasi-discrete module to study principally supplemented in general way. We prove that if R be principal ideal ring and if M be indecomposable R-module such that it has no maximal submodules (Rad(M) = M) then M is principally supplemented module. Also we prove that if M is indecomposable and local module then it is principally supplemented. Every projective module is self-projective therefore we prove that if M projective and supplemented module then M is principally supplemented. Key words: Principally supplemented, P-hollow module, f-lifting module, quasi-discrete module.
Highlights
Throughout this paper all rings have the identity and modules are considered to be right modules
The purpose of this paper is to further study the concept of a very important module theory namely principally supplemented modules
We will focus on quasi-discrete module to study principally supplemented in general way
Summary
Throughout this paper all rings have the identity and modules are considered to be right modules. A module M is called indecomposable if M ≠ 0, and it is not a direct sum of two nonzero submodules if R be principal ideal ring and M be indecomposable Rmodule with M = Rad(M) M is principally supplemented module.
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