Systems of parameters for a $K$-algebra

Asked Jul 23 '13 at 08:48

Active Jul 23 '13 at 09:47

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I don't know how to solve the next problem:

If we have two systems of parameters, $\{x_1,\ldots,x_n\}$ and $\{y_1,\ldots,y_n\}$ for a finitely generated $K$-algebra $A$ which is also an integral domain, and know that $A$ is free $K[x_1,\ldots,x_n]$-module how we prove that $A$ is free $K[y_1,\ldots,y_n]$-module?

System of parameters for $K$-algebra $A$ is an algebraically independent finite subset $\{x_1,\ldots,x_n\}$ of finite generated integral domain $A$ such that ring $A$ is integral over the polynomial subring $K[x_1,\ldots,x_n]$.

One should probably use Noether's normalization theorem.

Thank you very much for your help.

edited Jul 23 '13 at 09:12

asked Jul 23 '13 at 08:48

user87369

1

I never heard about such a definition of the systems of parameters. – Jul 27 '13 at 18:28
I have that definition in my textbook. – user87369 Jul 27 '13 at 20:37

Systems of parameters for a $K$-algebra

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