零维理想的仿射代数簇

摘要

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.%设K为一个域，I是多项式环K[x1，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K[x1，x2，…，xn]／I（V）及K[x1，x2，…，xn]／√I作为K上的向量空间时的维数之间的关系．