| On the Relation between Categories of Rings and Generalized Γ-rings |
| Received:April 04, 1987 |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1989.03.007 |
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