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 Mm,n , the M-ring T and the ring M2 are established.
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