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Year 2019, Volume 48 , Issue 4, Pages 973 - 984 2019-08-08

Abstract

Let $R$ be a ring and $M$ be an $R$-module. In this paper we investigate modules $M$ such that every (simple) cosingular $R$-module is $M$-projective. We prove that every simple cosingular module is $M$-projective if and only if for $N\leq T\leq M$, whenever $T/N$ is simple cosingular, then $N$ is a direct summand of $T$. We show that every simple cosingular right $R$-module is projective if and only if $R$ is a right $GV$-ring. It is also shown that for a right perfect ring $R$, every cosingular right $R$-module is projective if and only if $R$ is a right $GV$-ring. In addition, we prove that if every $\delta$-cosingular right $R$-module is semisimple, then $\overline{Z}(M)$ is a direct summand of $M$ for every right $R$-module $M$ if and only if $\overline{Z}_{\delta}(M)$ is a direct summand of $M$ for every right $R$-module $M$.

Keywords

projective module, cosingular module, $\delta$-cosingular module, $GV$-ring

References

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Details

Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0003-2311-4628
Author: Y. TALEBİ (Primary Author)

Orcid: 0000-0002-2852-7870
Author: A. R. M. HAMZEKOLAEE

Orcid: 0000-0003-1389-6419
Author: M. HOSSEİNPOUR

Orcid: 0000-0001-5691-933X
Author: A. HARMANCİ

Orcid: 0000-0001-7659-9185
Author: B. UNGOR
Dates

Publication Date : August 8, 2019

Cite

Bibtex @research article { hujms603492, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {973 - 984}, doi = {}, title = {Rings for which every cosingular module is projective}, key = {cite}, author = {Talebi̇, Y. and Hamzekolaee, A. R. M. and Hossei̇npour, M. and Harmanci̇, A. and Ungor, B.} }
APA Talebi̇, Y , Hamzekolaee, A , Hossei̇npour, M , Harmanci̇, A , Ungor, B . (2019). Rings for which every cosingular module is projective . Hacettepe Journal of Mathematics and Statistics , 48 (4) , 973-984 . Retrieved from https://dergipark.org.tr/en/pub/hujms/issue/47862/603492
MLA Talebi̇, Y , Hamzekolaee, A , Hossei̇npour, M , Harmanci̇, A , Ungor, B . "Rings for which every cosingular module is projective" . Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 973-984 <https://dergipark.org.tr/en/pub/hujms/issue/47862/603492>
Chicago Talebi̇, Y , Hamzekolaee, A , Hossei̇npour, M , Harmanci̇, A , Ungor, B . "Rings for which every cosingular module is projective". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 973-984
RIS TY - JOUR T1 - Rings for which every cosingular module is projective AU - Y. Talebi̇ , A. R. M. Hamzekolaee , M. Hossei̇npour , A. Harmanci̇ , B. Ungor Y1 - 2019 PY - 2019 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 973 EP - 984 VL - 48 IS - 4 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Rings for which every cosingular module is projective %A Y. Talebi̇ , A. R. M. Hamzekolaee , M. Hossei̇npour , A. Harmanci̇ , B. Ungor %T Rings for which every cosingular module is projective %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 4 %R %U
ISNAD Talebi̇, Y. , Hamzekolaee, A. R. M. , Hossei̇npour, M. , Harmanci̇, A. , Ungor, B. . "Rings for which every cosingular module is projective". Hacettepe Journal of Mathematics and Statistics 48 / 4 (August 2019): 973-984 .
AMA Talebi̇ Y , Hamzekolaee A , Hossei̇npour M , Harmanci̇ A , Ungor B . Rings for which every cosingular module is projective. Hacettepe Journal of Mathematics and Statistics. 2019; 48(4): 973-984.
Vancouver Talebi̇ Y , Hamzekolaee A , Hossei̇npour M , Harmanci̇ A , Ungor B . Rings for which every cosingular module is projective. Hacettepe Journal of Mathematics and Statistics. 2019; 48(4): 973-984.
IEEE Y. Talebi̇ , A. Hamzekolaee , M. Hossei̇npour , A. Harmanci̇ and B. Ungor , "Rings for which every cosingular module is projective", Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 4, pp. 973-984, Aug. 2019
Authors of the Article
Y. TALEBİ [1]
A. R. M. HAMZEKOLAEE [2]
M. HOSSEİNPOUR [3]
A. HARMANCİ [4]
B. UNGOR [5]
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