Article
| Title: | Rings generalized by tripotents and nilpotents (English) |
| Author: | Chen, Huanyin |
| Author: | Sheibani, Marjan |
| Author: | Ashrafi, Nahid |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 72 |
| Issue: | 4 |
| Year: | 2022 |
| Pages: | 1175-1182 |
| Summary lang: | English |
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| Category: | math |
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| 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). (English) |
| Keyword: | nilpotent |
| Keyword: | tripotent |
| Keyword: | 2-idempotent |
| Keyword: | exchange ring |
| MSC: | 13B99 |
| MSC: | 16E50 |
| MSC: | 16U99 |
| idZBL: | Zbl 07655792 |
| idMR: | MR4517605 |
| DOI: | 10.21136/CMJ.2022.0427-21 |
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| Date available: | 2022-11-28T11:42:34Z |
| Last updated: | 2023-04-11 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151139 |
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| Reference: | [1] Abyzov, A. N.: Strongly $q$-nil-clean rings.Sib. Math. J. 60 (2019), 197-208. Zbl 1461.16040, MR 3951146, 10.33048/smzh.2019.60.202 |
| Reference: | [2] Chen, H.: Rings Related Stable Range Conditions.Series in Algebra 11. World Scientific, Hackensack (2011). Zbl 1245.16002, MR 2752904, 10.1142/8006 |
| Reference: | [3] Chen, H., Sheibani, M.: Strongly 2-nil-clean rings.J. Algebra Appl. 16 (2017), Article ID 1750178, 12 pages. Zbl 1382.16035, MR 3661645, 10.1142/S021949881750178X |
| Reference: | [4] Danchev, P. V., Lam, T.-Y.: Rings with unipotent units.Publ. Math. 88 (2016), 449-466. Zbl 1374.16089, MR 3491753, 10.5486/PMD.2016.7405 |
| Reference: | [5] Diesl, A. J.: Nil clean rings.J. Algebra 383 (2013), 197-211. Zbl 1296.16016, MR 3037975, 10.1016/j.jalgebra.2013.02.020 |
| Reference: | [6] Koşan, M. T., Wang, Z., Zhou, Y.: Nil-clean and strongly nil-clean rings.J. Pure Appl. Algebra 220 (2016), 633-646. Zbl 1335.16026, MR 3399382, 10.1016/j.jpaa.2015.07.009 |
| Reference: | [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. Zbl 07128566, MR 4028489, 10.4153/S0008439519000092 |
| Reference: | [8] Koşan, M. T., Yildirim, T., Zhou, Y.: Rings with $x^n-x$ nilpotent.J. Algebra Appl. 19 (2020), Article ID 2050065, 14 pages. Zbl 1457.16036, MR 4098929, 10.1142/S0219498820500656 |
| Reference: | [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. Zbl 1373.16067, MR 3563747, 10.4153/CMB-2016-009-0 |
| Reference: | [10] Zhou, Y.: Rings in which elements are sums of nilpotents, idempotents and tripotents.J. Algebra Appl. 17 (2018), Article ID 1850009, 7 pages. Zbl 1415.16034, MR 3741066, 10.1142/S0219498818500093 |
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