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On Rings whose Quasi Projective Modules Are Projective or Semisimple

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Date

2021

Author

Orhan Ertaş, Nil
Acar, Ummahan

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Abstract

For two modules M and N, P-M(N) stands for the largest submodule of N relative to which M is projective. For any module M, P-M(N) defines a left exact preradical. It is given some properties of P-M(N). We express P-M(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, P-M(M) <=(e) M.

Source

Communications in Mathematics and Applications

Volume

12

Issue

2

URI

https://doi.org/10.26713/cma.v12i2.1490
https://hdl.handle.net/20.500.12809/9450

Collections

  • Matematik Bölümü Koleksiyonu [107]
  • WoS İndeksli Yayınlar Koleksiyonu [6466]



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