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## Simple continuous modules

#### Yongduo Wang [1]

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.
simple continuous module, singular simple-direct-injective module, $V$-ring, $GV$-ring
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Birincil Dil en Matematik Matematik Orcid: 0000-0002-0756-3899Yazar: Yongduo Wang (Sorumlu Yazar) Yayımlanma Tarihi : 8 Ekim 2019
 Bibtex @araştırma makalesi { hujms629829, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2019}, volume = {48}, pages = {1336 - 1344}, doi = {}, title = {Simple continuous modules}, key = {cite}, author = {Wang, Yongduo} } APA Wang, Y . (2019). Simple continuous modules. Hacettepe Journal of Mathematics and Statistics , 48 (5) , 1336-1344 . Retrieved from https://dergipark.org.tr/tr/pub/hujms/issue/49321/629829 MLA Wang, Y . "Simple continuous modules". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1336-1344 Chicago Wang, Y . "Simple continuous modules". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1336-1344 RIS TY - JOUR T1 - Simple continuous modules AU - Yongduo Wang Y1 - 2019 PY - 2019 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1336 EP - 1344 VL - 48 IS - 5 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Simple continuous modules %A Yongduo Wang %T Simple continuous modules %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 5 %R %U ISNAD Wang, Yongduo . "Simple continuous modules". Hacettepe Journal of Mathematics and Statistics 48 / 5 (Ekim 2019): 1336-1344 . AMA Wang Y . Simple continuous modules. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1336-1344. Vancouver Wang Y . Simple continuous modules. Hacettepe Journal of Mathematics and Statistics. 2019; 48(5): 1344-1336.