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Keywords:
nilpotent; tripotent; 2-idempotent; exchange ring
Summary:
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).
References:
[1] Abyzov, A. N.: Strongly $q$-nil-clean rings. Sib. Math. J. 60 (2019), 197-208. DOI 10.33048/smzh.2019.60.202 | MR 3951146 | Zbl 1461.16040
[2] Chen, H.: Rings Related Stable Range Conditions. Series in Algebra 11. World Scientific, Hackensack (2011). DOI 10.1142/8006 | MR 2752904 | Zbl 1245.16002
[3] Chen, H., Sheibani, M.: Strongly 2-nil-clean rings. J. Algebra Appl. 16 (2017), Article ID 1750178, 12 pages. DOI 10.1142/S021949881750178X | MR 3661645 | Zbl 1382.16035
[4] Danchev, P. V., Lam, T.-Y.: Rings with unipotent units. Publ. Math. 88 (2016), 449-466. DOI 10.5486/PMD.2016.7405 | MR 3491753 | Zbl 1374.16089
[5] Diesl, A. J.: Nil clean rings. J. Algebra 383 (2013), 197-211. DOI 10.1016/j.jalgebra.2013.02.020 | MR 3037975 | Zbl 1296.16016
[6] Koşan, M. T., Wang, Z., Zhou, Y.: Nil-clean and strongly nil-clean rings. J. Pure Appl. Algebra 220 (2016), 633-646. DOI 10.1016/j.jpaa.2015.07.009 | MR 3399382 | Zbl 1335.16026
[7] Koşan, M. T., Yildirim, T., Zhou, Y.: 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] Koşan, M. T., Yildirim, T., Zhou, Y.: 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] Ying, Z., Koşan, M. T., Zhou, Y.: 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] Zhou, Y.: 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
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