Note on strongly nil clean elements in rings
Aleksandra Kostić; Zoran Z. Petrović; Zoran S. Pucanović; Maja Roslavcev
Czechoslovak Mathematical Journal (2019)
- Volume: 69, Issue: 1, page 87-92
- ISSN: 0011-4642
Access Full Article
top
Abstract
topHow to cite
topKostić, Aleksandra, et al. "Note on strongly nil clean elements in rings." Czechoslovak Mathematical Journal 69.1 (2019): 87-92. <http://eudml.org/doc/294586>.
@article{Kostić2019,
abstract = {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.},
author = {Kostić, Aleksandra, Petrović, Zoran Z., Pucanović, Zoran S., Roslavcev, Maja},
journal = {Czechoslovak Mathematical Journal},
keywords = {nilpotent element; nil clean element},
language = {eng},
number = {1},
pages = {87-92},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Note on strongly nil clean elements in rings},
url = {http://eudml.org/doc/294586},
volume = {69},
year = {2019},
}
TY - JOUR
AU - Kostić, Aleksandra
AU - Petrović, Zoran Z.
AU - Pucanović, Zoran S.
AU - Roslavcev, Maja
TI - Note on strongly nil clean elements in rings
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 1
SP - 87
EP - 92
AB - 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.
LA - eng
KW - nilpotent element; nil clean element
UR - http://eudml.org/doc/294586
ER -
References
top- Chen, H., 10.4134/BKMS.2011.48.4.759, Bull. Korean Math. Soc. 48 (2011), 759-767. (2011) Zbl1233.16022MR2848142DOI10.4134/BKMS.2011.48.4.759
- Chen, H., 10.4134/BKMS.2012.49.3.589, Bull. Korean Math. Soc. 49 (2012), 589-599. (2012) Zbl1248.15012MR2963422DOI10.4134/BKMS.2012.49.3.589
- Chen, H., 10.1080/00927872.2011.637265, Commun. Algebra 41 (2013), 1074-1086. (2013) Zbl1286.16025MR3037180DOI10.1080/00927872.2011.637265
- Chen, H., Sheibani, M., 10.1080/00927872.2016.1222411, Commun. Algebra 45 (2017), 1719-1726. (2017) Zbl06715289MR3576689DOI10.1080/00927872.2016.1222411
- 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
- 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. (1988) Zbl0665.16016MR0976729
- Koşan, 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
- Šter, J., Rings in which nilpotents form a subring, Carpathian J. Math. 32 (2016), 251-258. (2016) MR3587893
NotesEmbed ?
topYou 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.