Rings Whose Certain Modules are Dual Self-CS-Baer

Year 2024, Volume: 12 Issue: 3, 113 - 118, 24.09.2024

Nuray Eroğlu

https://doi.org/10.36753/mathenot.1461857

https://izlik.org/JA38PA82WH

Abstract

In this work, we characterize some rings in terms of dual self-CS-Baer modules (briefly, ds-CS-Baer modules). We prove that any ring $R$ is a left and right artinian serial ring with $J^2(R)=0$ iff $R\oplus M$ is ds-CS-Baer for every right $R$-module $M$. If $R$ is a commutative ring, then we prove that $R$ is an artinian serial ring iff $R$ is perfect and every $R$-module is a direct sum of ds-CS-Baer $R$-modules. Also, we show that $R$ is a right perfect ring iff all countably generated free right $R$-modules are ds-CS-Baer.

Keywords

Dual self-CS-Baer module , Harada ring , Lifting module , Perfect ring , QF-ring , Serial ring

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