凯莱-哈密尔顿定理的一个广义扩张

A Generalized Extension of the Cayly-Hamilton Theorem

本文首先给出了在形式阵环M_n(R;s)上,凯莱-哈密尔顿定理的一个扩张.接着,我们也给出了凯莱-哈密尔顿定理两种情形下的广义扩张,一是,环R是整环.另一是,环R是一般交换环.

In this paper, Our intention is to give a generalization of an extension of the Cayley--Hamilton theorem in the case of two n × n matrices in the formal matrix ring/Vim （R ; s） . One case is two n × n formal matrices do not necessarily commute when R is an integral domain; the other is while R is a com- mutative ring, two n × n formal matrices do need to commute .