摘要
证明了整数环上任意方阵Ａ都可分解为一些整数环上行列式为１的初等矩阵与一个对角矩阵的乘积，且对角矩阵对角线上元素与原矩阵Ａ的所有元素具有相同的最大公因子，最后例举了这个定理的一些应用。
We prove that any squre matrix A on integral ring may be decomposed to the multiplication of some elementary matrices of determinant 1 and a diagonal matrix on the integral ring.Furthermore all diagonal elements of the diagonal matrix have the same maximal common factor as all elements of the matrix A.At last some application examples of this theorem are given.
