| 复合多项式的性质 |
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| 引用本文： | 李凤霞.复合多项式的性质[J].高师理科学刊,2011,31(2):40-42. |
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| 作者姓名： | 李凤霞 |
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| 作者单位： | 哈尔滨师范大学,恒星学院,信息科学系,黑龙江,哈尔滨,150025 |
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| 摘 要： | 探讨了复合多项式的性质,得到主要结论:设,是域,Fx]是F上关于未定元x的一元多项式环,f(x),g(x),h(x)∈Fx]次数都大于零,则h(f(x))=h(g(x))的充要条件是,f(x)=g(x)或者存在 1 的 m 次单位根ω∈F,使得f(x)=ωg(x)+r,h(x)=ck(x+r/ω-1)+…+c1(x...
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| 关 键 词： | 域 复合多项式 次数 单位根 |
Some properties of the composition of polynomials |
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| LI Feng-xia.Some properties of the composition of polynomials[J].Journal of Science of Teachers＇College and University,2011,31(2):40-42. |
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| Authors: | LI Feng-xia |
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| Institution: | LI Feng-xia(Department of Information Science,Star College,Harbin Normal University,Harbin 150025,China) |
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| Abstract: | Discussed some properties of the composition of polynomials,main conclusions as follow,let F be a number field,Fx] is a polynomial ring about indeterminate x over F,f（x）,g（x）,h（x） ∈Fx],the degree of f（x）,g（x）,h（x） are greater than zero,then h（f（x））=h（g（x）） if and only iff（x）=g（x） or there are ω∈F,where ω is anm-th root of unity in F,such that f（x）=ωg（x）＋r,h（x）=ck（x＋r/ω-1）km＋…＋c1（x＋r/ω-1）m＋c0,where m1,r∈F,k≥1,c0,…,ck∈F. |
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| Keywords: | number field composition of polynomial degree root of unity |
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