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## Rings such that, for each unit $u$, $u-u^n$ belongs to the Jacobson radical

#### M. Tamer KOŞAN [1] , Truong Cong QUYNH [2] , Tülay YILDIRIM [3] , Jan ŽEMLİČKA [4]

A ring $R$ is said to be $n$-UJ if $u-u^n\in J(R)$ for each unit $u$ of $R$, where $n > 1$ is a fixed integer. In this paper, the structure of $n$-UJ rings is studied under various conditions. Moreover, the $n$-UJ property is studied under some algebraic constructions.

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UU-ring, UJ-ring, unit, Jacobson radical, clean ring, (semi)regular ring, reduced ring
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Primary Language en Mathematics Mathematics Orcid: 0000-0002-5071-4568Author: M. Tamer KOŞAN (Primary Author)Institution: GAZI UNIVERSITYCountry: Turkey Orcid: 0000-0002-0845-0175Author: Truong Cong QUYNH Institution: The University of DanangCountry: Vietnam Orcid: 0000-0002-7289-5064Author: Tülay YILDIRIM Institution: GEBZE TECHNICAL UNIVERSITYCountry: Turkey Orcid: 0000-0003-3319-5193Author: Jan ŽEMLİČKA Institution: Charles UniversityCountry: Czech Republic Publication Date : August 6, 2020
 Bibtex @research article { hujms542574, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1397 - 1404}, doi = {10.15672/hujms.542574}, title = {Rings such that, for each unit \$u\$, \$u-u\^n\$ belongs to the Jacobson radical}, key = {cite}, author = {Koşan, M. Tamer and Quynh, Truong Cong and Yıldırım, Tülay and Žemli̇čka, Jan} } APA Koşan, M , Quynh, T , Yıldırım, T , Žemli̇čka, J . (2020). Rings such that, for each unit $u$, $u-u^n$ belongs to the Jacobson radical . Hacettepe Journal of Mathematics and Statistics , 49 (4) , 1397-1404 . DOI: 10.15672/hujms.542574 MLA Koşan, M , Quynh, T , Yıldırım, T , Žemli̇čka, J . "Rings such that, for each unit $u$, $u-u^n$ belongs to the Jacobson radical" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1397-1404 Chicago Koşan, M , Quynh, T , Yıldırım, T , Žemli̇čka, J . "Rings such that, for each unit $u$, $u-u^n$ belongs to the Jacobson radical". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1397-1404 RIS TY - JOUR T1 - Rings such that, for each unit $u$, $u-u^n$ belongs to the Jacobson radical AU - M. Tamer Koşan , Truong Cong Quynh , Tülay Yıldırım , Jan Žemli̇čka Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.542574 DO - 10.15672/hujms.542574 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1397 EP - 1404 VL - 49 IS - 4 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.542574 UR - https://doi.org/10.15672/hujms.542574 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Rings such that, for each unit $u$, $u-u^n$ belongs to the Jacobson radical %A M. Tamer Koşan , Truong Cong Quynh , Tülay Yıldırım , Jan Žemli̇čka %T Rings such that, for each unit $u$, $u-u^n$ belongs to the Jacobson radical %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 4 %R doi: 10.15672/hujms.542574 %U 10.15672/hujms.542574 ISNAD Koşan, M. Tamer , Quynh, Truong Cong , Yıldırım, Tülay , Žemli̇čka, Jan . "Rings such that, for each unit $u$, $u-u^n$ belongs to the Jacobson radical". Hacettepe Journal of Mathematics and Statistics 49 / 4 (August 2020): 1397-1404 . https://doi.org/10.15672/hujms.542574 AMA Koşan M , Quynh T , Yıldırım T , Žemli̇čka J . Rings such that, for each unit $u$, $u-u^n$ belongs to the Jacobson radical. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1397-1404. Vancouver Koşan M , Quynh T , Yıldırım T , Žemli̇čka J . Rings such that, for each unit $u$, $u-u^n$ belongs to the Jacobson radical. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1397-1404.

Authors of the Article
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