ON ESSENTIAL STRONG-NILPOTENCY OF #x3B3;-RINGS

摘要

An idealIof a #x393;-ringMis essential strongly-nilpotent ifIcontains a strongly-nilpotent idealNofMsuch thatK #x2229; N#x2260; 0 wheneverKis a non-zero ideal ofMcontained inI.LetMbe a #x393;-ring in the sense of Nobusawa. The ringM2=was defined by Kyuno. In this paper, the relationships between the unique largest essential strongly-nilpotent ideals of #x393;-ringMand the corresponding ideals of the right operator ringRofM, the matrix Tn,m-ringMm,n, theM-ringTand the ringM2are established.