query: When do we have $m\otimes n = 0$
positive_passages.docid: 145161
positive_passages.text: Testing whether an element of a tensor product of modules is zero
negative_passages.docid: 60804
negative_passages.text: About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
negative_passages.docid: 27248
negative_passages.text: If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
negative_passages.docid: 153107
negative_passages.text: Does every connected component of $\{z : |P(z)|<1 \}$ contain a zero?
negative_passages.docid: 53266
negative_passages.text: Show that $R/I\otimes_R R/J\cong R/(I+J)$
negative_passages.docid: 64500
negative_passages.text: $\aleph_1 = 2^{\aleph_0}$
negative_passages.docid: 89279
negative_passages.text: If $\sum a_n/k^n = 0$ for all $k$, then $a_n = 0$ for all $n$
negative_passages.docid: 35757
negative_passages.text: A 2x2 matrix $M$ exists. Suppose $M^3=0$ show that (I want proof) $M^2=0$
negative_passages.docid: 92876
negative_passages.text: Prove that $ \lim (s_n t_n) =0$ given $\vert t_n \vert \leq M $ and $ \lim (s_n) = 0$
negative_passages.docid: 18140
negative_passages.text: When does $\,n\mid q^3 \Rightarrow n\mid q\,$?
negative_passages.docid: 6874
negative_passages.text: smallest value of $k$ for which $a_k$ is $0$
negative_passages.docid: 53364
negative_passages.text: dim$(V)$ = $n$, dim$(W)$ = $m$ $\implies$ dim($L(V,W)$) = $nm$
negative_passages.docid: 42334
negative_passages.text: Does $\lambda$ $\mathbf u$ $= 0$ imply $\lambda = 0$ or $\mathbf u$ $= 0$?
negative_passages.docid: 16172
negative_passages.text: My proof of $I \otimes N \cong IN$ is clearly wrong, but where have I gone wrong?
negative_passages.docid: 141258
negative_passages.text: Why does $M \mathbin{\otimes_R} N \cong M_\mathfrak{p} \mathbin{\otimes_{R_\mathfrak{p}}} N$?
negative_passages.docid: 158343
negative_passages.text: how to prove an element is non-zero in a tensor-product
negative_passages.docid: 89533
negative_passages.text: $\mathcal{K}(L^2(\mathbb{R}^m \times \mathbb{R}^n)) = \mathcal{K}(L^2(\mathbb{R}^m)) \otimes \mathcal{K}(L^2(\mathbb{R}^n))$?