Year 2020, Volume 49 , Issue 5, Pages 1635 - 1648 2020-10-06

In this paper we introduce the concepts of $CD$-rings and $CD$-modules. Let $R$ be a ring and $M$ be an $R$-module. We call $R$ a $CD$-ring in case every cosingular $R$-module is discrete, and $M$ a $CD$-module if every $M$-cosingular $R$-module in $\sigma[M]$ is discrete. If $R$ is a ring such that the class of cosingular $R$-modules is closed under factor modules, then it is proved that $R$ is a $CD$-ring if and only if every cosingular $R$-module is semisimple. The relations of $CD$-rings are investigated with $V$-rings, $GV$-rings, $SC$-rings, and rings with all cosingular $R$-modules projective. If $R$ is a semilocal ring, then it is shown that $R$ is right $CD$ if and only if $R$ is left $SC$ with $Soc(_{R}R)$ essential in $_{R}R$. Also, being a $V$-ring and being a $CD$-ring coincide for local rings. Besides of these, we characterize $CD$-modules with finite hollow dimension.
CD-module, CD-ring, cosingular module, discrete module, V -ring, semilocal module, finite hollow dimension
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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0003-2311-4628
Author: Yahya TALEBİ
Institution: University of Mazandaran
Country: Iran


Orcid: 0000-0002-2852-7870
Author: Ali Reza MONİRİ HAMZEKOLAEE (Primary Author)
Institution: University of Mazandaran
Country: Iran


Orcid: 0000-0001-5691-933X
Author: Abdullah HARMANCI
Institution: HACETTEPE UNIVERSITY
Country: Turkey


Orcid: 0000-0001-7659-9185
Author: Burcu ÜNGÖR
Institution: ANKARA UNIVERSITY
Country: Turkey


Dates

Publication Date : October 6, 2020

Bibtex @research article { hujms500759, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1635 - 1648}, doi = {10.15672/hujms.500759}, title = {Rings for which every cosingular module is discrete}, key = {cite}, author = {Talebi̇, Yahya and Moni̇ri̇ Hamzekolaee, Ali Reza and Harmancı, Abdullah and Üngör, Burcu} }
APA Talebi̇, Y , Moni̇ri̇ Hamzekolaee, A , Harmancı, A , Üngör, B . (2020). Rings for which every cosingular module is discrete . Hacettepe Journal of Mathematics and Statistics , 49 (5) , 1635-1648 . DOI: 10.15672/hujms.500759
MLA Talebi̇, Y , Moni̇ri̇ Hamzekolaee, A , Harmancı, A , Üngör, B . "Rings for which every cosingular module is discrete" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1635-1648 <https://dergipark.org.tr/en/pub/hujms/issue/57199/500759>
Chicago Talebi̇, Y , Moni̇ri̇ Hamzekolaee, A , Harmancı, A , Üngör, B . "Rings for which every cosingular module is discrete". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1635-1648
RIS TY - JOUR T1 - Rings for which every cosingular module is discrete AU - Yahya Talebi̇ , Ali Reza Moni̇ri̇ Hamzekolaee , Abdullah Harmancı , Burcu Üngör Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.500759 DO - 10.15672/hujms.500759 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1635 EP - 1648 VL - 49 IS - 5 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.500759 UR - https://doi.org/10.15672/hujms.500759 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Rings for which every cosingular module is discrete %A Yahya Talebi̇ , Ali Reza Moni̇ri̇ Hamzekolaee , Abdullah Harmancı , Burcu Üngör %T Rings for which every cosingular module is discrete %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 5 %R doi: 10.15672/hujms.500759 %U 10.15672/hujms.500759
ISNAD Talebi̇, Yahya , Moni̇ri̇ Hamzekolaee, Ali Reza , Harmancı, Abdullah , Üngör, Burcu . "Rings for which every cosingular module is discrete". Hacettepe Journal of Mathematics and Statistics 49 / 5 (October 2020): 1635-1648 . https://doi.org/10.15672/hujms.500759
AMA Talebi̇ Y , Moni̇ri̇ Hamzekolaee A , Harmancı A , Üngör B . Rings for which every cosingular module is discrete. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1635-1648.
Vancouver Talebi̇ Y , Moni̇ri̇ Hamzekolaee A , Harmancı A , Üngör B . Rings for which every cosingular module is discrete. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1635-1648.