query: $2\otimes 1$ is non-zero in $2\mathbb Z\otimes_{\mathbb Z} \mathbb Z/2\mathbb Z$.
positive_passages.docid: 158343
positive_passages.text: how to prove an element is non-zero in a tensor-product
negative_passages.docid: 13794
negative_passages.text: $|z_{1} + z_{2}| = |z_{1} - z_{2}| \implies z_{1}/z_{2}$ is Imaginary
negative_passages.docid: 86807
negative_passages.text: The units of $\mathbb Z[\sqrt{2}]$
negative_passages.docid: 50596
negative_passages.text: $p_1p_2...p_n +1$ is not square for $p_k = k$'th prime
negative_passages.docid: 114152
negative_passages.text: Intermediate fields between $\mathbb{Z}_2 (\sqrt{x},\sqrt{y})$ and $\mathbb{Z}_2 (x,y)$
negative_passages.docid: 44307
negative_passages.text: Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
negative_passages.docid: 154305
negative_passages.text: Let $\pi$ denote a prime element in $\mathbb Z[i], \pi \notin \mathbb Z, i \mathbb Z$. Prove that $N(\pi)=2$ or $N(\pi)=p$, $p \equiv 1 \pmod 4$
negative_passages.docid: 53331
negative_passages.text: $\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
negative_passages.docid: 25195
negative_passages.text: $2 \otimes_{R} 2 + x \otimes_{R} x$ is not a simple tensor in $I \otimes_R I$
negative_passages.docid: 129750
negative_passages.text: Order of $SL_2(\mathbb{Z}/ n\mathbb{Z})$
negative_passages.docid: 146980
negative_passages.text: Zero divisors of $\mathbb{Z}×\mathbb{Z}×\mathbb{Z}$
negative_passages.docid: 153444
negative_passages.text: $\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
negative_passages.docid: 21840
negative_passages.text: Zero divisors and units for the ring $\mathbb{Z}/n\mathbb{Z}$ with integer $n$
negative_passages.docid: 129732
negative_passages.text: What is $\operatorname{Aut}(\mathbb{Z}_2\oplus \mathbb{Z}_2)$?
negative_passages.docid: 30752
negative_passages.text: Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
negative_passages.docid: 101164
negative_passages.text: Show that $B \cong \mathbb Z /2\mathbb Z$ for a Boolean field B
negative_passages.docid: 82262
negative_passages.text: minimal polynomial of nth root of 2 over $\mathbb Q$