ON RINGS IN WHICH ALL UNITS CAN BE PRESENTED IN THE FORM 𝟏 + 𝐞𝐑(𝟏 − 𝐞)

Abstract

The aim of the present paper is to characterize associative rings 𝑅 with unity in which 1 + 𝑒𝑅(1 − 𝑒) = 𝑈(𝑅) in terms of some important class of rings in the literature (for example, NR-rings, UU-rings, UJ-rings, UR-rings, exchange rings, 2-primal rings), where 𝑒2 = 𝑒 ∈ 𝑅 and 𝑈(𝑅) is the set of units of 𝑅.