ON ESSENTIAL STRONG-NILPOTENCY OF γ-RINGS

Abstract

An ideal I of a Γ-ring M is essential strongly-nilpotent if I contains a strongly-nilpotent ideal N of M such that K ∩ N ≠ 0 whenever K is a non-zero ideal of M contained in I. Let M be a Γ-ring in the sense of Nobusawa. The ring M₂ = was defined by Kyuno. In this paper, the relationships between the unique largest essential strongly-nilpotent ideals of Γ-ring M and the corresponding ideals of the right operator ring R of M, the matrix T _n,m -ring M_m,n , the M-ring T and the ring M₂ are established.