由n次幂等矩阵确定的Grothendieck群

Grothendieck Group from n-Potent Matrices

设R是含幺结合环,n≥2为自然数.给出了n次幂等矩阵集Pkn(R)={P|Pn=P∈Mk(R)}上的一个等价关系,并利用n次幂等矩阵的等价类得到了相关的Grothendieck群.

Let R be an associative ring, n≥2 be a natural number. In this paper, an equivalence relation on Pk^n（R）={P｜P^n=P∈Mk（R）} for all k≥ 1 is defined and a Grothendieck group using the defined equivalence classes is constructed.