User Koenraad van Duin

16 votes

3 answers

2k views

Error in proof: $\mathbb{C} \cong \mathbb{C} \times \mathbb{C}$??

asked Aug 1, 2013 at 20:42

11 votes

2 answers

3k views

Number of elements in the quotient ring $\mathbb{Z}[X]/(X^2-3, 2X+4)$

asked Jul 30, 2013 at 12:59

10 votes

5 answers

4k views

$\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD

asked Aug 13, 2013 at 20:44

10 votes

2 answers

1k views

Cosets modulo $(2+i)$ in $\mathbb{Z}[i]$

asked Jul 29, 2013 at 20:54

10 votes

1 answer

442 views

Could one make a ring of matrices of uncountable size?

asked Aug 10, 2014 at 18:12

9 votes

2 answers

388 views

$A_n \times \mathbb{Z} /2 \mathbb{Z} \ \ncong \ S_n$ for $n \geq 3$

asked Aug 3, 2014 at 20:39

8 votes

3 answers

3k views

How many irreducible monic quadratic polynomials are there in $\mathbb{F}_p[X]$?

asked Nov 7, 2013 at 22:30

8 votes

5 answers

5k views

$1^n +2^n + \cdots +(p-1)^n \mod p =$?

asked Oct 1, 2013 at 19:41

8 votes

1 answer

1k views

The structure of the group $(\mathbb{Z}/2^n\mathbb{Z})^*$

asked Aug 4, 2013 at 22:52

7 votes

1 answer

5k views

The trace map in a finite field.

asked Nov 28, 2013 at 21:56

7 votes

2 answers

625 views

If $\forall x \in R, x^2-x \in Z(G)$, than $R$ is commutative [duplicate]

asked Aug 23, 2014 at 13:16

6 votes

3 answers

272 views

Splitting $\Phi_{15}$ in irreducible factors over $\mathbb{F}_7$

asked Aug 25, 2014 at 21:09

6 votes

1 answer

78 views

The number of combinations $(a,b) \in \mathbb{Z}_n \times \mathbb{Z}_n$ such that $a \cdot b = 0$

asked Aug 28, 2014 at 12:31

6 votes

1 answer

588 views

To prove: $ [K : \mathbb{Q}] = 2 \ \Longrightarrow \ \exists \zeta \text{ primitive root of unity}, \ \mathbb{Q}(\zeta) \ \supseteq \ K $

asked Feb 21, 2015 at 23:05

6 votes

2 answers

282 views

The integral $\int_0^\infty \dfrac{x \sin(x)}{x^2+1} dx$

asked Jul 9, 2014 at 14:20

5 votes

5 answers

361 views

How to find $\sum_{k \in \mathbb{Z}}\frac1{(k+a)(k+b)}$

asked Jul 10, 2014 at 12:10

5 votes

3 answers

1k views

$H \lhd N \lhd G$ but $H \ntriangleleft G$ [duplicate]

asked Aug 3, 2014 at 13:24

5 votes

2 answers

120 views

If $\mathcal{B}^$ is a basis for $V^$, then $V^*$ is finite dimensional.

asked Sep 1, 2014 at 19:34

5 votes

1 answer

105 views

Is $U = \left\{A \in \mathbb{M}^ {n \times n}(\mathbb{R} ): \ker{A} \cap \text{Im}A = \{\vec{0}\} \right\}$ a vector space?

asked Dec 23, 2013 at 22:08

5 votes

3 answers

3k views

Let $R$ be a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal.

asked Aug 9, 2013 at 9:57

5 votes

2 answers

102 views

If $ a_n$ is increasingly divisible by $2$ and not a multiple of $10$ then the sum of its digits goes to infinity

asked Jul 10, 2016 at 9:40

4 votes

1 answer

396 views

Proving $\varprojlim S_i \ \cong \ \varprojlim S_j $ where $J \subseteq I$ cofinal.

asked Jul 10, 2016 at 8:28

4 votes

0 answers

515 views

To prove: The intersection of all normal subgroups of finite index of a free group is trivial.

asked Jul 15, 2016 at 18:45

4 votes

1 answer

150 views

Why is $\mathbb{F}_p[X]/(X^2+1)$ not a field if $p \equiv 1 \bmod4$

asked Aug 3, 2013 at 21:12

4 votes

1 answer

81 views

How to show that $n^{-r} \sum_{j=1}^n (X_j - \mu) \rightarrow 0$ in probability

asked Jan 29, 2014 at 19:54

4 votes

1 answer

3k views

The greatest common divisor of a polynomial and it's derivative

asked Dec 4, 2013 at 21:40

4 votes

4 answers

494 views

Infinitely many $n \in \mathbb{N}$ such that $\mu(n) + \mu(n+1) = 0 $.

asked Sep 13, 2014 at 20:23

4 votes

2 answers

82 views

finding $ \int_{C(0,2)^+} \frac{z^3}{z^3+z^2-z-1} $

asked Jul 6, 2014 at 7:56

3 votes

2 answers

58 views

A real matrix whith rows generating $U$ and columns generating $V$

asked Aug 11, 2014 at 19:33

3 votes

0 answers

106 views

$C_{\operatorname{Aut}(Q)}(\operatorname{Inn}(Q)) = \operatorname{Inn}(Q)$?

asked Aug 5, 2014 at 19:08

Stack Exchange Network

103 Questions

Error in proof: $\mathbb{C} \cong \mathbb{C} \times \mathbb{C}$??

Number of elements in the quotient ring $\mathbb{Z}[X]/(X^2-3, 2X+4)$

$\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD

Cosets modulo $(2+i)$ in $\mathbb{Z}[i]$

Could one make a ring of matrices of uncountable size?

$A_n \times \mathbb{Z} /2 \mathbb{Z} \ \ncong \ S_n$ for $n \geq 3$

How many irreducible monic quadratic polynomials are there in $\mathbb{F}_p[X]$?

$1^n +2^n + \cdots +(p-1)^n \mod p =$?

The structure of the group $(\mathbb{Z}/2^n\mathbb{Z})^*$

The trace map in a finite field.

If $\forall x \in R, x^2-x \in Z(G)$, than $R$ is commutative [duplicate]

Splitting $\Phi_{15}$ in irreducible factors over $\mathbb{F}_7$

The number of combinations $(a,b) \in \mathbb{Z}_n \times \mathbb{Z}_n$ such that $a \cdot b = 0$

To prove: $ [K : \mathbb{Q}] = 2 \ \Longrightarrow \ \exists \zeta \text{ primitive root of unity}, \ \mathbb{Q}(\zeta) \ \supseteq \ K $

The integral $\int_0^\infty \dfrac{x \sin(x)}{x^2+1} dx$

How to find $\sum_{k \in \mathbb{Z}}\frac1{(k+a)(k+b)}$

$H \lhd N \lhd G$ but $H \ntriangleleft G$ [duplicate]

If $\mathcal{B}^$ is a basis for $V^$, then $V^*$ is finite dimensional.

Is $U = \left\{A \in \mathbb{M}^ {n \times n}(\mathbb{R} ): \ker{A} \cap \text{Im}A = \{\vec{0}\} \right\}$ a vector space?

Let $R$ be a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal.

If $ a_n$ is increasingly divisible by $2$ and not a multiple of $10$ then the sum of its digits goes to infinity

Proving $\varprojlim S_i \ \cong \ \varprojlim S_j $ where $J \subseteq I$ cofinal.

To prove: The intersection of all normal subgroups of finite index of a free group is trivial.

Why is $\mathbb{F}_p[X]/(X^2+1)$ not a field if $p \equiv 1 \bmod4$

How to show that $n^{-r} \sum_{j=1}^n (X_j - \mu) \rightarrow 0$ in probability

The greatest common divisor of a polynomial and it's derivative

Infinitely many $n \in \mathbb{N}$ such that $\mu(n) + \mu(n+1) = 0 $.

finding $ \int_{C(0,2)^+} \frac{z^3}{z^3+z^2-z-1} $

A real matrix whith rows generating $U$ and columns generating $V$

$C_{\operatorname{Aut}(Q)}(\operatorname{Inn}(Q)) = \operatorname{Inn}(Q)$?