Mod—R(除环)到Mod—M_(Γ×Γ)(R)的完全忠实函子的存在性

On Existence of the Faithful and Full Functor F Mod--R to Mod--M_(г×г) (R) for a Division Ring R.

本文给出如下的定理,设R是一个除环,M_(Γ×Γ)(R)是R上的行有限的无限矩阵环,则对于模范畴Mod—R和Mod—M_(Γ×Γ)(R),存在完全忠实函子F:Mod—R→Mod—M_(Γ×Γ)(R)。这是保证两个模范畴等价的重要条件之一。

This paper presents the following theorem: let R be a divi-sion ring, M_(Г×Г).(R) the row finitely infinite matrix ring on R. This paperproved that there exisits a faithful and full functor F between the rightmodule categories Mod - R and Mod - M_(Г×Г)(R): Mod - R → Mod- M_(Г×Г)(R). This is one of the important conditions which provide twomodule categories equivalent.