query: Show that $\operatorname{Hom}_R(F,M)$ is isomorphic to $M^n$
positive_passages.docid: 153508
positive_passages.text: Define a function $\alpha$ :Hom$_R$($R^n,M$) $\rightarrow M^n$ which is a $R$-module isomorphism.
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: 66708
negative_passages.text: Elementary isomorphism between $\operatorname{PSL}(2,5)$ and $A_5$
negative_passages.docid: 102284
negative_passages.text: $GL(n,\mathbb R)/SL(n,\mathbb R)$ is isomophic to $\mathbb R^\times$
negative_passages.docid: 109267
negative_passages.text: Describe explicitly $\operatorname{Hom}_{\mathbb{Z}}(\mathbb{Z}_n, \mathbb{Z}_m)$.
negative_passages.docid: 145462
negative_passages.text: On the canonical isomorphism between $V$ and $V^{**}$
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: 68006
negative_passages.text: Find the dimensions of some kernel subspaces of $\operatorname{Hom}(V, W)$.
negative_passages.docid: 70576
negative_passages.text: Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
negative_passages.docid: 97608
negative_passages.text: Showing a Ring of endomorphisms is isomorphic to a Ring
negative_passages.docid: 91947
negative_passages.text: Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
negative_passages.docid: 18540
negative_passages.text: Isomorphism from $\mathbb{C}[G]$ to $\prod_{i=1}^h M_{n_i}(\mathbb{C})$.
negative_passages.docid: 83001
negative_passages.text: Easier way to show $(\mathbb{Z}/(n))[x]$ and $\mathbb{Z}[x] / (n)$ are isomorphic
negative_passages.docid: 75641
negative_passages.text: Is there a (f.g., free) module isomorphic to a quotient of itself?
negative_passages.docid: 40490
negative_passages.text: Birational isomorphism $\mathbb{P}^n\times \mathbb{P}^m\to \mathbb{P}^{n+m}$
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: 152212
negative_passages.text: Prove that the natural map $\alpha : \text{Hom}(X,\text{Spec} A) \rightarrow \text{Hom}(A,\Gamma(X,\mathcal{O}_X))$ is an isomorphism