On Rings Whose Quasi-Projective Modules Are Projective or Semisimple

Nil Orhan Ertas, Ummahan Acar


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 \(M\), \(P_M(M)\leq_e M\).


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

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DOI: http://dx.doi.org/10.26713%2Fcma.v12i2.1490


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