论文标题
Cohen-Macaulay代数的代数近似
Algebraic Approximation of Cohen-Macaulay Algebras
论文作者
论文摘要
本文表明，Cohen-Macaulay代数可以以代数近似，以使其Cohen-MaCaulayness和最少的Betti数字得以保留。这是通过证明在功率系列环上有限生成的模块可以以代数近似的方式来实现的，以保留其初始指数图和最小贝蒂数字的方式。这些结果还用于获得从功率序列到Cohen-Macaulay代数的平坦同态同态的近似结果。
This paper shows that Cohen-Macaulay algebras can be algebraically approximated in such a way that their Cohen-Macaulayness and minimal Betti numbers are preserved. This is achieved by showing that finitely generated modules over power series rings can be algebraically approximated in a manner that preserves their diagrams of initial exponents and their minimal Betti numbers. These results are also applied to obtain an approximation result for flat homomorphisms from rings of power series to Cohen-Macaulay algebras.
