与IBN指标相关的维定指标

DIMENSIONAL INDEX WITH RESPECT TO IBN INDEX

本文引进环的维定指标的概念,确立了环的维定指标与IBN指标的关系,证明了满足acc的环为维定环和强直有限环进而为IBN环,说明了维定环的左右不对称性,计算了一簇环的直积的维定指标和矩阵环的维定指标,推导了一些与维定指标有关的事实。

In this paper, we have defined dimensional indexes of rings, established the relation between dimensional index of ring and its IBN index, proved that a ring with acc is a dimensional, strong direct finite and IBN ring, shown that sometimes the left dimensional ring is not the right dimensional ring, calculated the dimensional index of direct product of a family of rings and the dimensional index of matrix ring, deduced some facts about dimensional index