| Title:
|
Note on strongly nil clean elements in rings (English) |
| Author:
|
Kostić, Aleksandra |
| Author:
|
Petrović, Zoran Z. |
| Author:
|
Pucanović, Zoran S. |
| Author:
|
Roslavcev, Maja |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
87-92 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be an associative unital ring and let $a\in R$ be a strongly nil clean element. We introduce a new idea for examining the properties of these elements. This approach allows us to generalize some results on nil clean and strongly nil clean rings. Also, using this technique many previous proofs can be significantly shortened. Some shorter proofs concerning nil clean elements in rings in general, and in matrix rings in particular, are presented, together with some generalizations of these results. (English) |
| Keyword:
|
nilpotent element |
| Keyword:
|
nil clean element |
| MSC:
|
13B25 |
| MSC:
|
15B33 |
| MSC:
|
16U99 |
| idZBL:
|
Zbl 07088771 |
| idMR:
|
MR3923576 |
| DOI:
|
10.21136/CMJ.2018.0167-17 |
| . |
| Date available:
|
2019-03-08T14:56:32Z |
| Last updated:
|
2021-04-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147619 |
| . |
| Reference:
|
[1] Chen, H.: Some strongly nil clean matrices over local rings.Bull. Korean Math. Soc. 48 (2011), 759-767. Zbl 1233.16022, MR 2848142, 10.4134/BKMS.2011.48.4.759 |
| Reference:
|
[2] Chen, H.: Strongly nil clean matrices over $R[x]/(x^2-1)$.Bull. Korean Math. Soc. 49 (2012), 589-599. Zbl 1248.15012, MR 2963422, 10.4134/BKMS.2012.49.3.589 |
| Reference:
|
[3] Chen, H.: On strongly nil clean matrices.Commun. Algebra 41 (2013), 1074-1086. Zbl 1286.16025, MR 3037180, 10.1080/00927872.2011.637265 |
| Reference:
|
[4] Chen, H., Sheibani, M.: On strongly nil clean rings.Commun. Algebra 45 (2017), 1719-1726. Zbl 06715289, MR 3576689, 10.1080/00927872.2016.1222411 |
| 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] Hirano, Y., Tominaga, H., Yaqub, A.: On rings in which every element is uniquely expressible as a sum of a nilpotent element and a certain potent element.Math. J. Okayama Univ. 30 (1988), 33-40. Zbl 0665.16016, MR 0976729 |
| Reference:
|
[7] Koşan, 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:
|
[8] Šter, J.: Rings in which nilpotents form a subring.Carpathian J. Math. 32 (2016), 251-258. MR 3587893 |
| . |
