Nilpotent-duo property on powers
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We study the structure of a generalization of right nilpotent-duo rings in relation with powers of elements. Such a ring property is said to be {\it weakly right nilpotent-duo}. We find connections between weakly right nilpotent-duo and weakly right duo rings, in several algebraic situations which have roles in ring theory. We also observe properties of weakly right nilpotent-duo rings in relation with their subrings and extensions.
Abstract
We study the structure of a generalization of right nilpotent-duo rings in relation with powers of elements. Such a ring property is said to be {\it weakly right nilpotent-duo}. We find connections between weakly right nilpotent-duo and weakly right duo rings, in several algebraic situations which have roles in ring theory. We also observe properties of weakly right nilpotent-duo rings in relation with their subrings and extensions.
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