分片代数集合的不可约性和同构

摘要

本文利用多元样条函数来定义分片代数集合,讨论了分片代数集合的不可约性和同构问题,给出了分片代数集合不可约的两个等价条件,并把分片代数集合的同构分类问题转化为交换代数的同构分类问题.%In this paper, we define the piecewise algebraic sets by using multivariate spline functions and discuss their irreducibility and isomorphism problem. We present two equivalent conditions for the irreducibility of piecewise algebraic sets, and turn the isomorphism and classifying problem of piecewise algebraic sets into the isomorphism and classifying problem of comnutative algebras.