query: Are $I\otimes_{R}J$ and $IJ$ isomorphic as $R$-modules?
positive_passages.docid: 16172
positive_passages.text: My proof of $I \otimes N \cong IN$ is clearly wrong, but where have I gone wrong?
negative_passages.docid: 43987
negative_passages.text: Decomposition of the tensor product $\mathbb{Q}_p \otimes_{\mathbb{Q}} \mathbb{Q}[i]$ into a product of fields
negative_passages.docid: 85752
negative_passages.text: Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules
negative_passages.docid: 8587
negative_passages.text: What is an example of two k-algebras that are isomorphic as rings, but not as k-algebras?
negative_passages.docid: 42810
negative_passages.text: Is $(\mathbb{Q},+)$ isomorphic to $(\mathbb{Q}^n,+)$?
negative_passages.docid: 60925
negative_passages.text: Why these are isomorphic each other for given these rings?
negative_passages.docid: 33781
negative_passages.text: Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?
negative_passages.docid: 118073
negative_passages.text: Is the ring $m\mathbb{Z}$ isomorphic to the ring $n\mathbb{Z}$?
negative_passages.docid: 73235
negative_passages.text: Rings $R/I \cong h(R)/h(I)\,$ for injective ring hom $h$
negative_passages.docid: 108955
negative_passages.text: Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
negative_passages.docid: 55148
negative_passages.text: Why is this isomorphism $M \otimes_K L \stackrel{\simeq}{\longrightarrow} M^{[L:K]}$ an isomorphism of $M$ - algebras?
negative_passages.docid: 158583
negative_passages.text: Prove that if $M$ is an $R-$ projective left module then $M/IM$ is an $R/I-$ projective left module.
negative_passages.docid: 78118
negative_passages.text: Algebraically, why is $\mathbb{Z}[i]/(i + 1)$ isomorphic to $\mathbb{Z}_{2}$?
negative_passages.docid: 84869
negative_passages.text: Are the groups $\mathbb{C}$ and $\mathbb{R}$ isomorphic?
negative_passages.docid: 109596
negative_passages.text: Isomorphism from $\mathrm{Aut}(\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z})$ to $S_3$
negative_passages.docid: 5996
negative_passages.text: Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?
negative_passages.docid: 72295
negative_passages.text: A difficulty in understanding the proof of distributivity of tensor products over direct sums for modules.