Gauss整数环Z[i]中元素的最大公因子及其求法  

Greatest Common Factor of Elements in the Gauss Integral Ring Z[i]and Its Solution

作　　者：张景晓[1] 

机构地区：[1]德州学院数学系,山东德州253023

出　　处：《德州学院学报》2011年第2期15-17,共3页Journal of Dezhou University

摘　　要：证明了Gauss整数环Z[i]中非零元素在映射φ的作用下的最小值的原像α0~1,由此给出了求Z[i]中元素最大公因子的两种方法：辗转相除法和矩阵的广义初等变换法.We proved α0~1,where α0 is preimage of nonzero elements in Z[i],and image of this nonzero elements under φ is equal to minimum value.Two methods of calculating greatest common factor of elements in Z[i] were given,that is division algorithm and generalized elementary transformation of matrix.

关 键 词：Gauss整数环Z[i] 最大公因子 广义初等变换 

分 类 号：O153.3[理学—数学]