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Rad-supplemented modules

Engin Büyükaşik; Engin Mermut; Salahattin Özdemir — 2010

Rendiconti del Seminario Matematico della Università di Padova

Rings whose nonsingular right modules are $R$ -projective

Yusuf Alagöz; Sinem Benli; Engin Büyükaşık — 2021

Commentationes Mathematicae Universitatis Carolinae

A right $R$ -module $M$ is called $R$ -projective provided that it is projective relative to the right $R$ -module $R_{R}$ . This paper deals with the rings whose all nonsingular right modules are $R$ -projective. For a right nonsingular ring $R$ , we prove that $R_{R}$ is of finite Goldie rank and all nonsingular right $R$ -modules are $R$ -projective if and only if $R$ is right finitely $Σ$ - $C S$ and flat right $R$ -modules are $R$ -projective. Then, $R$ -projectivity of the class of nonsingular injective right modules is also considered. Over right...

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Rad-supplemented modules

Rings whose nonsingular right modules are R -projective

Rings whose nonsingular right modules are $R$ -projective