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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 2

On a generalization of $C_2$-modules

Abdoul Djibril Diallo(Université Cheikh Anta Diop de Dakar)0000-0002-1791-0639
Papa Cheikhou Dıop(Université de Thiès)0000-0003-0628-0018
Rachid Tribak(Centre Régional des Métiers de l'Education et de la Formation (CRMEF-TTH)-Tanger)0000-0001-8400-4321
Sayfa
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Yayın Tarihi
2022-04-01
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Also, we prove that for a ring $R$, every $R$-module has $(C_{21})$ if and only if $R$ is a right t-semisimple ring.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:A module $M$ is called a $C_{21}$-module if, whenever $A$ and $B$ are submodules of $M$ with $A \cong B$, $A$ is nonsingular and $B$ is a direct summand of $M$, then $A$ is a direct summand of $M$.
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Temel Bulgular & Veri:Various examples of $C_{21}$-modules are presented.
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Sonuç & Katkı:Also, we prove that for a ring $R$, every $R$-module has $(C_{21})$ if and only if $R$ is a right t-semisimple ring.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:$C_{21}$-module · $C_2$-module · nonsingular module

Abstract

A module $M$ is called a $C_{21}$-module if, whenever $A$ and $B$ are submodules of $M$ with $A \cong B$, $A$ is nonsingular and $B$ is a direct summand of $M$, then $A$ is a direct summand of $M$. Various examples of $C_{21}$-modules are presented. Some basic properties of these modules are investigated. It is shown that the class of rings $R$ over which every $C_{21}$-module is a $C_2$-module is exactly that of right SI-rings. Also, we prove that for a ring $R$, every $R$-module has $(C_{21})$ if and only if $R$ is a right t-semisimple ring.

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Bu Makaleye Atıf Yap

Diallo, A. D., Dıop, P. C., Tribak, R. (2022). On a generalization of $C_2$-modules. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 2. https://doi.org/10.15672/hujms.792212

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