Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1706-79
Keywords
Quasinilpotent, nilpotent, idempotent, local ring, Boolean ring
First Page
2854
Last Page
2862
Recommended Citation
CUI, J (2018). Quasinilpotents in rings and their applications. Turkish Journal of Mathematics 42 (5): 2854-2862. https://doi.org/10.3906/mat-1706-79
