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Czechoslovak Mathematical Journal, Vol. 72, No. 4, pp. 1175-1182, 2022

Rings generalized by tripotents and nilpotents

Huanyin Chen, Marjan Sheibani, Nahid Ashrafi

Received November 15, 2021.   Published online May 6, 2022.
Abstract:  We present new characterizations of the rings for which every element is a sum of two tripotents and a nilpotent that commute. These extend the results of Z. L. Ying, M. T. Koşan, Y. Zhou (2016) and Y. Zhou (2018).
Keywords:  nilpotent; tripotent; 2-idempotent; exchange ring
Classification MSC:  16E50, 13B99, 16U99
DOI:  10.21136/CMJ.2022.0427-21
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References:
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[7] M. T. Koşan, T. Yildirim, Y. Zhou: Rings whose elements are the sum of a tripotent and an element from the Jacobson radical. Can. Math. Bull. 62 (2019), 810-821. DOI 10.4153/S0008439519000092 | MR 4028489 | Zbl 07128566
[8] M. T. Koşan, T. Yildirim, Y. Zhou: Rings with $x^n-x$ nilpotent. J. Algebra Appl. 19 (2020), Article ID 2050065, 14 pages. DOI 10.1142/S0219498820500656 | MR 4098929 | Zbl 1457.16036
[9] Z. Ying, M. T. Koşan, Y. Zhou: Rings in which every element is a sum of two tripotents. Can. Math. Bull. 59 (2016), 661-672. DOI 10.4153/CMB-2016-009-0 | MR 3563747 | Zbl 1373.16067
[10] Y. Zhou: Rings in which elements are sums of nilpotents, idempotents and tripotents. J. Algebra Appl. 17 (2018), Article ID 1850009, 7 pages. DOI 10.1142/S0219498818500093 | MR 3741066 | Zbl 1415.16034
Affiliations:   Huanyin Chen, School of Mathematics, Hangzhou Normal University, Yuhangtang Road, Yuhang District, 311121, Hangzhou, Zhejiang, P. R. China, e-mail: huanyinchen@aliyun.com; Marjan Sheibani (corresponding author), Farzanegan Campus, Semnan University, Semnan, Iran, e-mail: m.sheibani@semnan.ac.ir; Nahid Ashrafi, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran, e-mail: nashrafi@semnan.ac.ir
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[List of online first articles] [Contents of Czechoslovak Mathematical Journal] [Full text of the older issues of Czechoslovak Mathematical Journal at DML-CZ]
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