Turkish Journal of Mathematics
DOI
10.3906/mat-1706-79
Abstract
An element $a$ of an associative ring $R$ is said to be quasinilpotent if $1-ax$ is invertible for every $x\in R$ with $xa=ax$. Nilpotents and elements in the Jacobson radical of a ring are well-known examples of quasinilpotents. In this paper, properties and examples of quasinilpotents in a ring are provided, and the set of quasinilpotents is applied to characterize rings with some certain properties.
Keywords
Quasinilpotent, nilpotent, idempotent, local ring, Boolean ring
First Page
2854
Last Page
2862
Recommended Citation
CUI, JIAN
(2018)
"Quasinilpotents in rings and their applications,"
Turkish Journal of Mathematics: Vol. 42:
No.
5, Article 60.
https://doi.org/10.3906/mat-1706-79
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss5/60
