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.
Dual self-CS-Baer module Harada ring Lifting module Perfect ring QF-ring Serial ring
Birincil Dil | İngilizce |
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Konular | Uygulamalı Matematik (Diğer) |
Bölüm | Articles |
Yazarlar | |
Erken Görünüm Tarihi | 30 Nisan 2024 |
Yayımlanma Tarihi | |
Gönderilme Tarihi | 30 Mart 2024 |
Kabul Tarihi | 30 Nisan 2024 |
Yayımlandığı Sayı | Yıl 2024 Cilt: 12 Sayı: 3 |
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