## Tagged Questions

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### objects which can’t be defined without making choices but which end up independent of the choice

It happens a lot of times that when one defines a new object (ring, module, space, group, algebra, morphism, whatever) out of given data one first chooses some additional structure …
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### How many Perfect Matchings in a regular bipartite Graph

Hi Guys, We have a d-regular bipartite Graph $G = (X,Y,E)$ with $|X| = |Y| = n$ and $|E| = nd$. i want to know a Upper Bound of the number of Matching Thankx
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### Permutations of $(Z/pZ)^*$

Let $p$ be a prime integer, and let $(\mathbb Z/p\mathbb Z)^*$ be the set of non-zero elements of $\mathbb Z/p \mathbb Z$. Denote by $S((\mathbb Z/p \mathbb Z)^*)$ the group of per …
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### Uniformly converge?

I'm not sure wether or not the following sum uniformly converge on $\mathbb{R}$ : $$\sum_{n=1}^{\infty} \frac{\sin(n x) \sin(n^2 x)}{n+x^2}$$ Can someone help me with it? (I can' …
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### Is a Cauchy principal value invariant under a “change of variables”?

Let $f \in C^{\gamma}_c(\mathbb{R}^n)$. Let $K:\mathbb{R}^n \backslash {\vec{0}} \rightarrow \mathbb{R}^n$ be a singular integral kernel with the following properties: 1) K smoot …
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### Why do rigid spaces have “not enough points”?

In Brian Conrad's notes here for the 2007 Arizona winter school, bottom of p18, he says that there is an affinoid rigid-analytic space and a sheaf of abelian groups on it equipped …
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### decomposition of the injective hull of a torsion free module

Let $R$ be a ring, $\Sigma$ be a multiplicatively closed subset of $R$. $M$ is an $R$-module. Denote the injective hull of $M$ by $E(M)$. $M$ is $\Sigma$-torsion if for any $m$ …
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### The question has been deleted [closed]

Hello, The question is deleted (I did not know how to do it, that is why I needed to edit the question and write at least 15 characters)