所有同态象其Jacobson根与单根相同的Γ-环

设M是Nobusawa意义下的Г-环,S.Kyuno定义了环M_2=其中R,L分别是M的右、左算子环.本文首先刻画了环M_2的本原理想与Ja-cobson根.其次引进了一类新的Г-环称为PM Г-环,建立了Г-环M、矩阵Г_(n,m)-环M_(m,n)、Г-环M的右(左)算子环R(L)、M-环Г及M_2的PM性质之间的关系.最后,给出了Г-环一般形式的Jacobson性质,Jacobson性质、Brown-McCoy性质以及PM性质为其特殊情况.

Γ-Rings for Which the Jacoboson Radical Equals the Simplical Radical in All Homomorphic Images

Let M be a Γ-ring in the sense of Nobusawa.The ring M2=(RΓML) was defined by Kyuno. In this paper, first we characterise primitive ideals and the Jacobson radical of M2. Next, we introduce a new class of Γ-rings in which, for every homomorphic image, the Jacobson radical equals the simplicial radical. We shall call this the class of PM-Γ-rings. Relationships between PM properties of Γ-ring M and the corresponding properties of Γn,m-ring Mm,n, the right operator ring R of Γ-ring M, M-ring Γ and the ring M2 are established. Finally, we give a general version of Jacobson properties for Γ-rings, which includes also Jacobson property, Brown-McCoy property and PM property.