关于对偶模Euler特征数的注记

REMARKS ON EULER CHARACTERISTIC NUMBER OF DUAL MODULES

本文研究了对偶模的Euler特征数,引进了环的Euler对偶维数,进而给出了环的一种新的分类方法。

In this paper, we studied Euler characteristic numbers, and introduced Euler dual dimensions. Moreover, we obtained the following results: ed. dimR=0 iff X(P*) =X(P) for any P∈FFR. Let ed. dimR≤1, P∈FR. Then X(P*)=X(P) iff X(Ext1(P, R))=0.This method will give us a new tool to classify general rings.