query: $(S_f)_0$ is a finitely generated algebra if $S$ is.
positive_passages.docid: 114267
positive_passages.text: If $S$ is a finitely generated graded algebra over $S_0$, $S_{(f)}$ is finitely generated algebra over $S_0$?
negative_passages.docid: 149412
negative_passages.text: Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
negative_passages.docid: 17304
negative_passages.text: Tensor product of two finitely-generated modules over a local ring is zero
negative_passages.docid: 62615
negative_passages.text: If F is a finite field, then $F^F=P_F$.
negative_passages.docid: 44065
negative_passages.text: If $B$ is finitely generated as a $k$-algebra, and $\phi:A\to B$ is a $k$-algebra map, is $\phi^{-1}(M)$ maximal for any maximal $M\subset B$?
negative_passages.docid: 91947
negative_passages.text: Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
negative_passages.docid: 140553
negative_passages.text: An ideal which is not finitely generated
negative_passages.docid: 53432
negative_passages.text: What is the algebraic closure of $\mathbb F_q$?
negative_passages.docid: 78350
negative_passages.text: When does a finite ring become a finite field?
negative_passages.docid: 37570
negative_passages.text: $M + N$ and $M \cap N$ are finitely generated $A$-modules implies $M$ and $N$ finitely generated using exact sequences
negative_passages.docid: 93474
negative_passages.text: A Finite Boolean Ring is Generated by Finitely Many Copies of $\mathbb{Z} / 2 \mathbb{Z}$
negative_passages.docid: 153622
negative_passages.text: Are intermediate rings of finitely generated ring extensions also finitely generated?
negative_passages.docid: 1251
negative_passages.text: If $[G:K]$ is finite, then $[H:H \cap K] = [G:K]$ iff $G = HK$ (Hungerford Proposition 4.8, Proof)
negative_passages.docid: 14259
negative_passages.text: If M+N and M$\cap$N are finitely generated modules, so are M and N.
negative_passages.docid: 9806
negative_passages.text: $M$ finitely generated if submodule and quotient are finitely generated.
negative_passages.docid: 43814
negative_passages.text: What does it mean when a set is said to be a "finitely generated vector space"?
negative_passages.docid: 104233
negative_passages.text: Is the ring of the polynomials on a finite algebraic set always a product of local rings?