query: How to show that $ \left(k[\textbf{x}]/I\right)\otimes_k\left(k[\textbf{y}]/J\right)\cong k[\textbf{x},\textbf{y}]/(I^e+J^e)$?
positive_passages.docid: 147564
positive_passages.text: Why does $(A/I)\otimes_R (B/J)\cong(A\otimes_R B)/(I\otimes_R 1+1\otimes_R J)$?
negative_passages.docid: 135046
negative_passages.text: Can this quick way of showing that $K[X,Y]/(Y-X^2)\cong K[X]$ be turned into a valid argument?
negative_passages.docid: 96380
negative_passages.text: Representation of $\text{sl}(2,\mathbb{C})$
negative_passages.docid: 111129
negative_passages.text: Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
negative_passages.docid: 53687
negative_passages.text: Why is $\text{Hom}(V,W)$ the same thing as $V^* \otimes W$?
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: 19424
negative_passages.text: Showing $(M^\perp)^\perp=\overline{M}$
negative_passages.docid: 23517
negative_passages.text: Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group
negative_passages.docid: 157074
negative_passages.text: The elements in the composite field $FK$
negative_passages.docid: 61993
negative_passages.text: Why is $V^{\vee}\otimes W^{\vee}\longrightarrow (V\otimes W)^{\vee}$ always injective?
negative_passages.docid: 146300
negative_passages.text: Fast way to create $[ I_4\otimes e_1,\ \dots ,\ I_4 \otimes e_T]$?
negative_passages.docid: 62123
negative_passages.text: Proving that Tensor Product is Associative
negative_passages.docid: 132653
negative_passages.text: How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple?
negative_passages.docid: 24585
negative_passages.text: Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
negative_passages.docid: 102175
negative_passages.text: $Z=XY$, $E_Z[Z]$, $E_{X,Y}[XY]$
negative_passages.docid: 2235
negative_passages.text: Showing $\text{Aut}_\mathsf{Grp}(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}) \cong S_3$
negative_passages.docid: 117131
negative_passages.text: Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$