Rings such that, for each unit u, u - un belongs to the Jacobson radical

Abstract

A ring R is said to be n-UJ if u - u(n) is an element of J(R) for each unit u of R, where n > 1 is a fixed integer. In this paper, the structure of n-UJ rings is studied under various conditions. Moreover, the n-UJ property is studied under some algebraic constructions.