Quasinilpotents in rings and their applications
Authors : Jian Cui
Pages : 2854-2862
View : 7 | Download : 6
Publication Date : 9999-12-31
Article Type : Makaleler
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