| 零维理想的仿射代数簇 |
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| 引用本文： | 何苗,尹久元.零维理想的仿射代数簇[J].达县师范高等专科学校学报,2011(5):15-18. |
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| 作者姓名： | 何苗 尹久元 |
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| 作者单位： | 电子科技大学应用数学学院,四川成都611731 |
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| 摘 要： | 设K为一个域，I是多项式环Kx1，x2，…，xn]上的零维理想．研究了，的仿射代数簇V（I）中包含的点至多的个数及其等价命题，V（I）中包含的点的个数与商环Kx1，x2，…，xn]／I（V）及Kx1，x2，…，xn]／√I作为K上的向量空间时的维数之间的关系．
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| 关 键 词： | 零维理想 仿射代数簇 商环 |
On Affine Varieties of Zero Dimensional Ideals |
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| Institution: | HE Miao,YIN Jiu - yuan (Applied Mathematics College of Electronic and Technology University, Chengdu Sichuan 611731, China) |
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| Abstract: | If K is a field and I is a zero dimensional ideal in the polynomial ring K x1 ,x2 , .., xn] , the number of poims is studied on the affine variety of V（I） in I at most and its equivalem conditions. The relation is studied between the number of points of V（I） and the dimension of quotient ring K x1 ,x2 ..., xn ]/I（V） and the dimension of quotient ring K x1 ,x2 ,..., xn ]/I where the dimension means dimension as a vector space over K. |
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| Keywords: | zero dimensional ideal atone variety quotient ring |
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