| 域k上三次一般方程式的解的计算 |
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| 引用本文： | 裴晓雯,吴茂全,吴会咏.域k上三次一般方程式的解的计算[J].沈阳航空工业学院学报,2010,27(1):87-88,71. |
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| 作者姓名： | 裴晓雯 吴茂全 吴会咏 |
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| 作者单位： | 沈阳化工学院数理系,辽宁,沈阳,110142 |
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| 摘 要： | 我们已经研究了域k上的n（n≥5）次一般方程在特征标为0的情形下关于幂根是不可解的，而对于n≤4是可解的。本文利用n次循环域的拉格朗日分解式及循环群σ∈G（K/k）的结构，推出域k上的三次一般方程在特征标为0的情形下一般解的计算公式。
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| 关 键 词： | n次对称群 n次交代群 拉格朗日分解式 |
Solve calculation of degree 3 equation on field |
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| PEI Xiao-wen,WU Mao-quan,WU Hui-yong.Solve calculation of degree 3 equation on field[J].Journal of Shenyang Institute of Aeronautical Engineering,2010,27(1):87-88,71. |
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| Authors: | PEI Xiao-wen WU Mao-quan WU Hui-yong |
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| Institution: | PEI Xiao - wen WU Mao -quan WU Hui - yong ( Shenyang Institute of Chemical Technology, Liaoning Shenyang 110142) |
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| Abstract: | We have discussed the general equation of degree n（n≥5） on the field is unsolvable, when character is zero. It is solvable for the general equation of degree n （n≤ 4）. This paper shall make use of Lagrange, s solve of the circulating field with degree n and the structure of circulating group σ ∈ G （K/k）, the calculated formula of the general equation of degree 3 on the field k shall be derived, when character is zero. |
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| Keywords: | symmetric group of degree alternation group of degree Lagrange＇ solve |
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