Rings generalized by tripotents and nilpotents

Huanyin Chen; Marjan Sheibani; Nahid Ashrafi

Czechoslovak Mathematical Journal (2022)

  • Volume: 72, Issue: 4, page 1175-1182
  • ISSN: 0011-4642

Abstract

top
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).

How to cite

top

Chen, Huanyin, Sheibani, Marjan, and Ashrafi, Nahid. "Rings generalized by tripotents and nilpotents." Czechoslovak Mathematical Journal 72.4 (2022): 1175-1182. <http://eudml.org/doc/298908>.

@article{Chen2022,
abstract = {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).},
author = {Chen, Huanyin, Sheibani, Marjan, Ashrafi, Nahid},
journal = {Czechoslovak Mathematical Journal},
keywords = {nilpotent; tripotent; 2-idempotent; exchange ring},
language = {eng},
number = {4},
pages = {1175-1182},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Rings generalized by tripotents and nilpotents},
url = {http://eudml.org/doc/298908},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Chen, Huanyin
AU - Sheibani, Marjan
AU - Ashrafi, Nahid
TI - Rings generalized by tripotents and nilpotents
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 4
SP - 1175
EP - 1182
AB - 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).
LA - eng
KW - nilpotent; tripotent; 2-idempotent; exchange ring
UR - http://eudml.org/doc/298908
ER -

References

top
  1. Abyzov, A. N., 10.33048/smzh.2019.60.202, Sib. Math. J. 60 (2019), 197-208. (2019) Zbl1461.16040MR3951146DOI10.33048/smzh.2019.60.202
  2. Chen, H., 10.1142/8006, Series in Algebra 11. World Scientific, Hackensack (2011). (2011) Zbl1245.16002MR2752904DOI10.1142/8006
  3. Chen, H., Sheibani, M., 10.1142/S021949881750178X, J. Algebra Appl. 16 (2017), Article ID 1750178, 12 pages. (2017) Zbl1382.16035MR3661645DOI10.1142/S021949881750178X
  4. Danchev, P. V., Lam, T.-Y., 10.5486/PMD.2016.7405, Publ. Math. 88 (2016), 449-466. (2016) Zbl1374.16089MR3491753DOI10.5486/PMD.2016.7405
  5. Diesl, A. J., 10.1016/j.jalgebra.2013.02.020, J. Algebra 383 (2013), 197-211. (2013) Zbl1296.16016MR3037975DOI10.1016/j.jalgebra.2013.02.020
  6. Koşan, M. T., Wang, Z., Zhou, Y., 10.1016/j.jpaa.2015.07.009, J. Pure Appl. Algebra 220 (2016), 633-646. (2016) Zbl1335.16026MR3399382DOI10.1016/j.jpaa.2015.07.009
  7. Koşan, M. T., Yildirim, T., Zhou, Y., 10.4153/S0008439519000092, Can. Math. Bull. 62 (2019), 810-821. (2019) Zbl07128566MR4028489DOI10.4153/S0008439519000092
  8. Koşan, M. T., Yildirim, T., Zhou, Y., 10.1142/S0219498820500656, J. Algebra Appl. 19 (2020), Article ID 2050065, 14 pages. (2020) Zbl1457.16036MR4098929DOI10.1142/S0219498820500656
  9. Ying, Z., Koşan, M. T., Zhou, Y., 10.4153/CMB-2016-009-0, Can. Math. Bull. 59 (2016), 661-672. (2016) Zbl1373.16067MR3563747DOI10.4153/CMB-2016-009-0
  10. Zhou, Y., 10.1142/S0219498818500093, J. Algebra Appl. 17 (2018), Article ID 1850009, 7 pages. (2018) Zbl1415.16034MR3741066DOI10.1142/S0219498818500093

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.