| Gauss整数环Z[i]中元素的最大公因子及其求法 |
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| 引用本文： | 张景晓.Gauss整数环Z[i]中元素的最大公因子及其求法[J].德州学院学报,2011,27(2):15-17. |
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| 作者姓名： | 张景晓 |
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| 作者单位： | 德州学院数学系,山东德州,253023 |
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| 摘 要： | 证明了Gauss整数环Zi]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Zi]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.
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| 关 键 词： | Gauss整数环Z[i] 最大公因子 广义初等变换 |
Greatest Common Factor of Elements in the Gauss Integral Ring Z[i]and Its Solution |
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| ZHANG Jing-xiao.Greatest Common Factor of Elements in the Gauss Integral Ring Z[i]and Its Solution[J].Journal of Dezhou University,2011,27(2):15-17. |
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| Authors: | ZHANG Jing-xiao |
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| Institution: | ZHANG Jing-xiao(Department of Mathematics,Dezhou University,Dezhou Shandong 253023,China) |
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| Abstract: | We proved α0~1,where α0 is preimage of nonzero elements in Zi],and image of this nonzero elements under φ is equal to minimum value.Two methods of calculating greatest common factor of elements in Zi] were given,that is division algorithm and generalized elementary transformation of matrix. |
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| Keywords: | Gauss integral Ring Z[i] greatest common factor generalized elementary transformation |
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