与IBN指标相关的维定指标

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。

DIMENSIONAL INDEX WITH RESPECT TO IBN INDEX

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