对R中元素a ≠ 0,考虑一列元素a,a^2,a^3,...由R的元素个数有限,存在m > n使a^m = a^n,设b = a^(m-n),即有a^n·(b-1) = 0.若b = 1,则a^(m-n-1)·a = a·a^(m-n-1) = b = 1,a可逆.若b ≠ 1,取最小的正整数k使a^k·(b-1...