Almost nilpotent gamma rings

Abstract

In this paper we introduce the concept of almost nilpotence for Γ-rings, similar to the corresponding concept for rings, as defined by Van Leeuwen and Heyman. An almost mlpotent radical property Α0 is introduced for Γ-rings, and shown to be supernilpotent. If M is a Γ-ring with left and right operator rings L and R respectively, then Α(L)+ = Α0(M) = Α(R)*, where Α(−) denotes the almost nilpotent radical of a ring. If M is a Γ-ring and m, n are positive integers, then Α0(Mm, n) is the almost nilpotent radical of the Γn, m-ring Mm, n.