On Rings Whose Quasi-Projective Modules Are Projective or Semisimple

Authors

  • Nil Orhan Ertas Department of Mathematics, Bursa Technical University, Bursa
  • Ummahan Acar Department of Mathematics, Mugla Sıtkı Koçman University, Mugla

DOI:

https://doi.org/10.26713/cma.v12i2.1490

Keywords:

Projective module, p-poor module, Projectivity domain, Semi-Artininan ring

Abstract

For two modules  M and N, PM(N) stands for the largest submodule of N relative to which M is projective. For any module M, PM(N) defines a left exact preradical. It is given some properties of PM(N).\ We express PM(N) as a trace submodule. In this paper, we study rings with no quasi-projective modules other than semisimples and projectives, that is, rings whose quasi-projectives are either projective or semisimple (namely QPS-ring). Semi-Artinian rings and rings with no right p-middle class are characterized by using this functor: a ring R right semi-Artinian if and only if for any right R-module M, PM(M)≤eM.

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References

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Published

30-06-2021
CITATION

How to Cite

Ertas, N. O., & Acar, U. (2021). On Rings Whose Quasi-Projective Modules Are Projective or Semisimple. Communications in Mathematics and Applications, 12(2), 295–302. https://doi.org/10.26713/cma.v12i2.1490

Issue

Vol. 12 No. 2 (2021)

Section

Research Article

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