query: Prove that there is a natural bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
positive_passages.docid: 145722
positive_passages.text: Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
negative_passages.docid: 151993
negative_passages.text: Ring homomorphisms $\mathbb Z[x]\rightarrow \mathbb Q$
negative_passages.docid: 40490
negative_passages.text: Birational isomorphism $\mathbb{P}^n\times \mathbb{P}^m\to \mathbb{P}^{n+m}$
negative_passages.docid: 141984
negative_passages.text: Find the number of homomorphisms between $\mathbb{Z}_m$ and $\mathbb{Z}_n$
negative_passages.docid: 31391
negative_passages.text: bijection between $\mathbb{N}$ and $\mathbb{N}\times\mathbb{N}$
negative_passages.docid: 64140
negative_passages.text: Find a bijection from $\mathbb R$ to $\mathbb R-\mathbb N$
negative_passages.docid: 114916
negative_passages.text: $\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
negative_passages.docid: 102299
negative_passages.text: Bijection between $\mathbb{R}^n$ and $\mathbb{R}^m$
negative_passages.docid: 97608
negative_passages.text: Showing a Ring of endomorphisms is isomorphic to a Ring
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
negative_passages.docid: 150986
negative_passages.text: For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
negative_passages.docid: 37479
negative_passages.text: Proper submodules of Noetherian modules are intersections of indecomposable modules
negative_passages.docid: 108028
negative_passages.text: Is there a bijection between the reals and naturals?
negative_passages.docid: 59687
negative_passages.text: Suppose $M$ is a finitely generated module over $R$ where $R$ is a Noetherian ring. Prove that $M$ is a noetherian module.
negative_passages.docid: 23125
negative_passages.text: Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
negative_passages.docid: 30327
negative_passages.text: $\ker \phi = (x_1-a_1, ..., x_n-a_n)$ for a ring homomorphism $\phi: R[x_1, ..., x_n] \to R$
negative_passages.docid: 37570
negative_passages.text: $M + N$ and $M \cap N$ are finitely generated $A$-modules implies $M$ and $N$ finitely generated using exact sequences