| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2022-11-28T11:42:34Z |
| Last updated:
|
2025-01-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151139 |
| . |
| 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 |
| . |
