query: $A$ algebra of finite type over $\mathbb{Z}$, $\mathfrak{m}$ max ideal implies $A/\mathfrak{m}$ is a finite field?
positive_passages.docid: 29635
positive_passages.text: Fields finitely generated as $\mathbb Z$-algebras are finite?
negative_passages.docid: 119305
negative_passages.text: Is the splitting field equal to the quotient $k[x]/(f(x))$ for finite fields?
negative_passages.docid: 140553
negative_passages.text: An ideal which is not finitely generated
negative_passages.docid: 30714
negative_passages.text: A question on ring homomorphisms and maximal ideals.
negative_passages.docid: 105818
negative_passages.text: Given an associative $F$-algebra do there necessarily exist elements $a_1,a_2 \in K$ satisfying $a_1*a_2=a$?
negative_passages.docid: 57123
negative_passages.text: Jacobson radical of a finitely generated $\mathbb Z$-algebra is nilpotent
negative_passages.docid: 112150
negative_passages.text: Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
negative_passages.docid: 67796
negative_passages.text: How to prove that the algebra $k[x, xy, xy^2, xy^3, \dotsc]$ is not finitely generated?
negative_passages.docid: 53770
negative_passages.text: Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
negative_passages.docid: 150206
negative_passages.text: Every finitely generated algebra over a field is a Jacobson ring
negative_passages.docid: 41895
negative_passages.text: Show $\text{Hom}_{Ab}(A,\mathbb{Q}) = \{0\}$ for finite $A$
negative_passages.docid: 109688
negative_passages.text: Zero-dimensional ideals and finite-dimensional algebras
negative_passages.docid: 16643
negative_passages.text: A slick proof that a field which is finitely generated as a ring is finite
negative_passages.docid: 19230
negative_passages.text: Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
negative_passages.docid: 9806
negative_passages.text: $M$ finitely generated if submodule and quotient are finitely generated.
negative_passages.docid: 104486
negative_passages.text: Ideal in $\mathbb Z[x]$ which is not two-generated
negative_passages.docid: 75970
negative_passages.text: $\mathbb Z[1/2]$ is not finitely generated?