关于环作为Γ－环的根

On Radicals of a Ring Regarded as a Gamma Ring

证明了如果Ｍ是一个环，具有素根Ｐ（Ｍ），底座Ｓｏｃ（Ｍ），诣零根Ｎ（Ｍ）和Ｌｅｖｉｔｚｋｉ诣零根Ｌ（Ｍ），则Ｍ作为一个Γ－环（取Γ＝Ｍ）有：Ｐ（Ｍ）＝ＰΓ（Ｍ），Ｓｏｃ（Ｍ）＝ＳｏｃΓ（Ｍ），Ｎ（Ｍ）＝Ｎｒ（Ｍ）和Ｌ（Ｍ）＝ＬΓ（Ｍ）

This paper show: if M is a ring with the prime radiCal P(M), the socle Soc(M),the nil radical N(M) and the Levitzki nil radical L(M),then regarded as a Pring with P=M,Pp(M)=P(M),Socp(M)=Soc(M),Np(M)=N(M) and LP(M)=L(M).