[대수기하] 2. Hilbert Basis Theorem
Hilbert basis Theorem. If a Comm. ring $R$ is Necterim. then so is $R[x]$. In partialar, $k\left[x_{1}, \cdots, x_{n}\right]$ is Nötherian. Consequentity, for each $\sin k\left[x_{1}, \cdots, x_{n}\right]$, $(S)=\left(f_{1}, \cdots, f_{r}\right)$ for some $f_{1}, \cdots$, fr $\in S$. Ex $k$ field $\Rightarrow k:$ Noettlerian. Lemma R Comm. ing. TFAE: (1) Every ideal in $R$ Can be generated by fi..
2023. 7. 2.