Geodesic
Rings generalized by tripotents and nilpotents
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 1175-1182
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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).
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).
DOI : 10.21136/CMJ.2022.0427-21
Classification : 13B99, 16E50, 16U99
Keywords: nilpotent; tripotent; 2-idempotent; exchange ring 
@article{10_21136_CMJ_2022_0427_21,
     author = {Chen, Huanyin and Sheibani, Marjan and Ashrafi, Nahid},
     title = {Rings generalized by tripotents and nilpotents},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1175--1182},
     year = {2022},
     volume = {72},
     number = {4},
     doi = {10.21136/CMJ.2022.0427-21},
     mrnumber = {4517605},
     zbl = {07655792},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0427-21/}
}
TY  - JOUR
AU  - Chen, Huanyin
AU  - Sheibani, Marjan
AU  - Ashrafi, Nahid
TI  - Rings generalized by tripotents and nilpotents
JO  - Czechoslovak Mathematical Journal
PY  - 2022
SP  - 1175
EP  - 1182
VL  - 72
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0427-21/
DO  - 10.21136/CMJ.2022.0427-21
LA  - en
ID  - 10_21136_CMJ_2022_0427_21
ER  - 
%0 Journal Article
%A Chen, Huanyin
%A Sheibani, Marjan
%A Ashrafi, Nahid
%T Rings generalized by tripotents and nilpotents
%J Czechoslovak Mathematical Journal
%D 2022
%P 1175-1182
%V 72
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0427-21/
%R 10.21136/CMJ.2022.0427-21
%G en
%F 10_21136_CMJ_2022_0427_21
Chen, Huanyin; Sheibani, Marjan; Ashrafi, Nahid. Rings generalized by tripotents and nilpotents. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 1175-1182. doi: 10.21136/CMJ.2022.0427-21

[1] Abyzov, A. N.: Strongly $q$-nil-clean rings. Sib. Math. J. 60 (2019), 197-208. | DOI | MR | JFM

[2] Chen, H.: Rings Related Stable Range Conditions. Series in Algebra 11. World Scientific, Hackensack (2011). | DOI | MR | JFM

[3] Chen, H., Sheibani, M.: Strongly 2-nil-clean rings. J. Algebra Appl. 16 (2017), Article ID 1750178, 12 pages. | DOI | MR | JFM

[4] Danchev, P. V., Lam, T.-Y.: Rings with unipotent units. Publ. Math. 88 (2016), 449-466. | DOI | MR | JFM

[5] Diesl, A. J.: Nil clean rings. J. Algebra 383 (2013), 197-211. | DOI | MR | JFM

[6] Koşan, M. T., Wang, Z., Zhou, Y.: Nil-clean and strongly nil-clean rings. J. Pure Appl. Algebra 220 (2016), 633-646. | DOI | MR | JFM

[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 | MR | JFM

[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 | MR | JFM

[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 | MR | JFM

[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 | MR | JFM

Cité par Sources :