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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 5

Simple continuous modules

Yongduo Wang0000-0002-0756-3899
Sayfa
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Yayın Tarihi
2019-10-08
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

For instance, it is shown that a ring $R$ is a right $V$-ring if and only if every right $R$-module is a simple continuous modules, and that a regular ring $R$ is a right $GV$-ring if and only if every cyclic right $R$-module is a singular simple-direct-injective module.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:A module $M$ is called a simple continuous module if it satisfies the conditions $(min-C_{1})$ and $(min-C_{2})$.
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Temel Bulgular & Veri:A module $M$ is called singular simple-direct-injective if for any singular simple submodules $A$, $B$ of $M$ with $A\cong B\mid M$, then $A\mid M$.
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Sonuç & Katkı:For instance, it is shown that a ring $R$ is a right $V$-ring if and only if every right $R$-module is a simple continuous modules, and that a regular ring $R$ is a right $GV$-ring if and only if every cyclic right $R$-module is a singular simple-direct-injective module.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:simple continuous module · singular simple-direct-injective module · $V$-ring

Abstract

A module $M$ is called a simple continuous module if it satisfies the conditions $(min-C_{1})$ and $(min-C_{2})$. A module $M$ is called singular simple-direct-injective if for any singular simple submodules $A$, $B$ of $M$ with $A\cong B\mid M$, then $A\mid M$. Various basic properties of these modules are proved, and some well-studied rings are characterized using simple continuous modules and singular simple-direct-injective modules. For instance, it is shown that a ring $R$ is a right $V$-ring if and only if every right $R$-module is a simple continuous modules, and that a regular ring $R$ is a right $GV$-ring if and only if every cyclic right $R$-module is a singular simple-direct-injective module.

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Bu Makaleye Atıf Yap

Wang, Y. (2019). Simple continuous modules. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 5. https://ajindex.com/articles/1402733

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