query: $\mathbb Q$ is not finitely generated $\mathbb Z$-algebra
positive_passages.docid: 29635
positive_passages.text: Fields finitely generated as $\mathbb Z$-algebras are finite?
negative_passages.docid: 53331
negative_passages.text: $\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
negative_passages.docid: 85586
negative_passages.text: Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
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: 137285
negative_passages.text: Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$
negative_passages.docid: 143831
negative_passages.text: Showing $\mathbb{Q}$ is homeomorphic to $\mathbb{Q}^2$
negative_passages.docid: 17748
negative_passages.text: Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?
negative_passages.docid: 17378
negative_passages.text: Characterize finite dimensional algebras without nilpotent elements
negative_passages.docid: 80202
negative_passages.text: Why is $[0, 1] \cap \mathbb{Q}$ not compact in $\mathbb{Q}$?
negative_passages.docid: 51687
negative_passages.text: Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
negative_passages.docid: 151993
negative_passages.text: Ring homomorphisms $\mathbb Z[x]\rightarrow \mathbb Q$
negative_passages.docid: 55026
negative_passages.text: $\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
negative_passages.docid: 66020
negative_passages.text: What is $\mathbb Z[[t]]$? What are the double brackets?
negative_passages.docid: 2719
negative_passages.text: Why isn't an infinite direct product of copies of $\Bbb Z$ a free module?
negative_passages.docid: 86015
negative_passages.text: $\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
negative_passages.docid: 14003
negative_passages.text: $(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$
negative_passages.docid: 57310
negative_passages.text: Prove $\mathbb{Z}$ is not a vector space over a field