分次Γ－环的J－根、底座和链条件

Jacobson Radicals, Socles and Chain Conditions of Gamma Rings

证明了Ｚ－型分次Γ－环的Ｊａｃｏｂｓｏｎ根和底座是分次理想，得到一系列有关分次Γ－环的分次Ｊ－根（分次底座）与Ｊ－根（底座）之间的关系式，并给出Γ－环的链条件的一些基本结果．

This paper shows that the Jacobson radical and socle of a graded gamma ring of type Z are graded ideals, obtains some relations between the graded Jacobson radical(graded socle) and the Jacobson radical (socle) of a graded gamma ring, and gives some basic results of chain conditions of a gamma ring.