THE STRONGLY PRIME RADICAL OF A GMA RING

Abstract

A notion of strongly prime is introduced for Γ-rings, and the class of strongly prime Γ-rings is shown to be special. Let M be a Γ-ring with left and right operator rings L and R, respectively. It is shown that s(L)⁺ = s_o (M), and if M has both unities, then s(R)* = s_o(M). where s() and s_o() denote the strongly prime radical of a ring and a Γ-ring respectively. If m and n are positive integers, then s_o (M_mn) = s_o (M)_mn, where M_mn denotes the set of ▪ x n matrices over M. considered as a Γa_mn -ring. The relationship of s_o(M) with the other radicals of M is discussed.