On the Relation between Categories of Rings and Generalized Γ-rings

DOI：10.3770/j.issn:1000-341X.1989.03.007

 作者 单位 陈维新 浙江大学数学系

以R表示具有乘法单位元的结合环范畴,这里obR是结合环类,态射是保持单位元的环同态。以GΓR表示具有乘法单位元的广义Γ-环范畴,这里obGΓR是广义Γ-环类,态射是保持单位元的广义Γ-环同态。本文证明了:R和GΓR是等价的。

In his lecture at International Conference in Austria, Kyuno, S. expounded the relation between categories of rings and Γn-rings. In this paper we generalize his ideas to the investigation of the generalized Γ-ring that is more general than the Γn-ring, We study the relation between categories of rings and generalized Γ-rings. The following are proved.Theorem R and GΓR are equivalent. Here R is the category of associative rings with unity for multiplication, GΓR is the category of generalized Γ-rings with unity for multiplication. Lemma GΓR and SGR are equivalent. Here SGR is the category of Γn-ring with strong unity for multiplication. From these results, it is made clear that Γn-ring, generalized Γ-rings and associative ring are quite close each other. Thus the generalized Γ-ring is really good generalization of associative ring and Γn-ring.