Γ—环的广义诣零根及RΓ—模刻划

ON THE GENERALIZATION OF NIL RADICAL OF г-RINGS AND ITS CHARACTERIZATION OF R-MODULES

本文在结合Γ—环中引进了广义诣零根Ng的概念,证明了Ng是个遗传根,得到了Ng—半单Γ—环的结构定理,并用RΓ—模对广义诣零根Ng进行了模刻划。本文是一般结合环根理论的推广,结合环中某些熟知结果已成为本文的特款。

The concept of generalized nil radical Ng is introduced into associative г-rings in this article. With Ng being proved to be a hereditary radical, the structurs theorem of Ng-semisimple г-rings is affirmed, and by means of Rг-modules, the generalized nil radical Ng is characterized. The article represents a development of the general associative ring radical theory; it features some of the well-known results of associative rings.