User Xindaris

13 votes

2 answers

6k views

Fundamental group of two tori with a circle ($S^1✕${$x_0$}) identified

asked Sep 13, 2014 at 18:06

12 votes

6 answers

4k views

Possible flaw in "proof" that a sum of two compact operators is compact

asked Nov 7, 2014 at 20:58

11 votes

2 answers

7k views

Cauchy convergence in probability implies the existence of a (finite a.e.) limit $X$

asked Oct 6, 2014 at 15:22

7 votes

1 answer

880 views

Maximal ideal not containing the set of powers of an element is prime

asked Jan 16, 2014 at 2:34

7 votes

1 answer

3k views

Any ring is integral over the subring of invariants under a finite group action

asked Apr 1, 2014 at 22:32

6 votes

1 answer

1k views

For a distribution function $F(x)$ and constant $a$, integral of $F(x + a) - F(x)$ is $a$.

asked Oct 4, 2014 at 18:17

6 votes

2 answers

3k views

Obtaining Wirtinger presentation using van Kampen theorem

asked Sep 12, 2014 at 17:26

5 votes

2 answers

2k views

Rigorous Covering Space Construction

asked Sep 22, 2014 at 16:59

5 votes

1 answer

2k views

How does one actually take the dual of a chain complex?

asked Nov 21, 2014 at 16:25

5 votes

1 answer

897 views

If ring $B$ is integral over $A$, then an element of $A$ which is a unit in $B$ is also a unit in $A$.

asked Mar 30, 2014 at 16:34

5 votes

2 answers

2k views

Define the dual group $\hat G$ as the set of all homs. from $G$ to $\Bbb C^*$, with pointwise multiplication. Show $\hat G$ is an abelian group.

asked Sep 25, 2013 at 1:18

5 votes

0 answers

315 views

Proof of the classifying space cohomology isomorphism for local coefficients

asked May 25, 2020 at 15:28

4 votes

0 answers

963 views

sup of integrals of simple functions = inf of integrals of simple functions implies f is measurable?

asked Feb 21, 2015 at 19:34

4 votes

2 answers

2k views

Monotone increasing continuous function with $\int_a^b f' = f(b) - f(a)$ which is not absolutely continuous

asked Apr 9, 2015 at 22:11

4 votes

1 answer

145 views

If $0 < r < p < \infty$, then $\|f\|_r \leq (\frac{p}{p-r})^{1/r} \mu(X)^{1/r - 1/p} \|f\|_{p, w}$ (weak $L^p$ norm)

asked Feb 20, 2016 at 21:09

4 votes

1 answer

1k views

Express quotient of free abelian group as direct sum of cyclic groups

asked Sep 22, 2013 at 23:06

4 votes

2 answers

2k views

If a commutative ring with identity is the sum of two ideals, then their product is equal to their intersection.

asked Oct 8, 2013 at 0:38

4 votes

4 answers

3k views

Example of a commutative ring with identity with two ideals whose product is not equal to their intersection

asked Oct 9, 2013 at 23:12

4 votes

3 answers

699 views

Proving $\mathbb{F}_p[x]/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements

asked Oct 28, 2013 at 0:23

4 votes

2 answers

3k views

Show that $\ker(f)$ is finitely generated, when $f: M \rightarrow A^n$ is a surjective $A$-module homomorphism and $M$ is finitely generated

asked Jan 29, 2014 at 15:33

4 votes

1 answer

2k views

How to show that homotopy of chain maps respects composition?

asked Nov 16, 2014 at 18:01

3 votes

1 answer

226 views

Constructing a surjection from fundamental group of a mapping cone to Hawaiian Earring to $\prod_\infty \mathbb{Z} / \oplus_\infty \mathbb{Z}$

asked Sep 8, 2014 at 15:56

3 votes

2 answers

189 views

If for $A$ a commutative nonzero ring $A^m ≅ A^n$ as $A$-modules, then $m = n$

asked Jan 31, 2014 at 15:22

3 votes

2 answers

1k views

Finish a proof that every prime ideal of a ring is the contraction of a prime ideal in its formal power series

asked Jan 24, 2014 at 18:38

3 votes

2 answers

538 views

"Primeness" of C[x] in B[x], where A is a subring of B and C is the integral closure of A in B. [Dedekind's Prague Theorem]

asked Apr 2, 2014 at 15:50

3 votes

1 answer

1k views

With B integral over subring A, homomorphism from A to algebraically closed field F can be extended to B.

asked Apr 6, 2014 at 14:08

3 votes

2 answers

2k views

$1 +\sqrt{-n}$ is irreducible in $\mathbb{Z}[\sqrt{-n}]$

asked Oct 27, 2013 at 4:11

3 votes

0 answers

752 views

Any set of $d$ points in projective space is the zero locus of polynomials of degree $d - 1$

asked Oct 16, 2015 at 16:49

3 votes

1 answer

1k views

Wrong answer? Irreducible components of $Y$ defined by $x^2 - yz$ and $xz - x$

asked Oct 21, 2015 at 17:26

3 votes

1 answer

588 views

"Intermediate value theorem" for Lebesgue integrals and subsets

asked Mar 5, 2015 at 21:34

Stack Exchange Network

96 Questions

Fundamental group of two tori with a circle ($S^1✕${$x_0$}) identified

Possible flaw in "proof" that a sum of two compact operators is compact

Cauchy convergence in probability implies the existence of a (finite a.e.) limit $X$

Maximal ideal not containing the set of powers of an element is prime

Any ring is integral over the subring of invariants under a finite group action

For a distribution function $F(x)$ and constant $a$, integral of $F(x + a) - F(x)$ is $a$.

Obtaining Wirtinger presentation using van Kampen theorem

Rigorous Covering Space Construction

How does one actually take the dual of a chain complex?

If ring $B$ is integral over $A$, then an element of $A$ which is a unit in $B$ is also a unit in $A$.

Define the dual group $\hat G$ as the set of all homs. from $G$ to $\Bbb C^*$, with pointwise multiplication. Show $\hat G$ is an abelian group.

Proof of the classifying space cohomology isomorphism for local coefficients

sup of integrals of simple functions = inf of integrals of simple functions implies f is measurable?

Monotone increasing continuous function with $\int_a^b f' = f(b) - f(a)$ which is not absolutely continuous

If $0 < r < p < \infty$, then $\|f\|_r \leq (\frac{p}{p-r})^{1/r} \mu(X)^{1/r - 1/p} \|f\|_{p, w}$ (weak $L^p$ norm)

Express quotient of free abelian group as direct sum of cyclic groups

If a commutative ring with identity is the sum of two ideals, then their product is equal to their intersection.

Example of a commutative ring with identity with two ideals whose product is not equal to their intersection

Proving $\mathbb{F}_p[x]/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements

Show that $\ker(f)$ is finitely generated, when $f: M \rightarrow A^n$ is a surjective $A$-module homomorphism and $M$ is finitely generated

How to show that homotopy of chain maps respects composition?

Constructing a surjection from fundamental group of a mapping cone to Hawaiian Earring to $\prod_\infty \mathbb{Z} / \oplus_\infty \mathbb{Z}$

If for $A$ a commutative nonzero ring $A^m ≅ A^n$ as $A$-modules, then $m = n$

Finish a proof that every prime ideal of a ring is the contraction of a prime ideal in its formal power series

"Primeness" of C[x] in B[x], where A is a subring of B and C is the integral closure of A in B. [Dedekind's Prague Theorem]

With B integral over subring A, homomorphism from A to algebraically closed field F can be extended to B.

$1 +\sqrt{-n}$ is irreducible in $\mathbb{Z}[\sqrt{-n}]$

Any set of $d$ points in projective space is the zero locus of polynomials of degree $d - 1$

Wrong answer? Irreducible components of $Y$ defined by $x^2 - yz$ and $xz - x$

"Intermediate value theorem" for Lebesgue integrals and subsets