User Noah Olander

15 votes

What is a short exact sequence?

answered Jun 25, 2016 at 13:47

11 votes

Prove the open mapping theorem by using maximum modulus principle

answered Mar 31, 2015 at 1:30

8 votes

Accepted

Automorphism group of an infinite field.

answered Dec 23, 2015 at 18:12

7 votes

Accepted

Are these conditions sufficient for a $\mathbb{Z}$-module to be free?

answered May 18, 2016 at 6:47

7 votes

Accepted

Prove the set of matrices with one Jordan block is not dense in $M_n(\mathbb{C}).$

answered Sep 1, 2016 at 3:21

7 votes

Accepted

Why must a meromorphic function, bounded near infinity, have the same number of poles and zeros?

answered Dec 20, 2015 at 21:50

6 votes

Accepted

Looking for a Better Way to Think About Polynomial Rings

answered Jun 9, 2015 at 22:41

6 votes

Is the zero ideal $\{0_{M_2(\mathbb{R})}\}$ maximal in $M_{2}(\mathbb{R})$?

answered Apr 21, 2015 at 0:08

6 votes

Accepted

Prove that there exists a real number $x$ for which $\displaystyle \sum_{k=0}^n a_kx^k = 0$

answered Mar 14, 2016 at 22:32

6 votes

Accepted

Open set containing rationals but complement non-denumerable

answered Dec 25, 2015 at 6:23

5 votes

If $f(x,y)\in R[x,y]$ is an irreducible polynomial, is $R[x,y]/f(x,y)$ a field?

answered Jan 7, 2016 at 17:35

5 votes

Accepted

Does $f$ have a limit if $\lim_{x\to\infty}f'(x)=0$?

answered Jan 10, 2016 at 16:56

5 votes

Accepted

Continuous homorphisms between topological groups.

answered Jun 9, 2015 at 18:15

5 votes

If a function $f$ is holomorphic on the closed unit disk centered at the origin and is real valued whenever $|z| = 1$, then $f$ is constant.

answered Jul 6, 2016 at 16:28

5 votes

Accepted

$(f(x))^p\neq f(x^p)$ on infinite field of characteristic $p$

answered Jun 5, 2015 at 4:46

5 votes

Accepted

Algebraic numbers are a field

answered Jun 6, 2015 at 5:50

5 votes

Is this quotient of a disk Hausdorff?

answered Jun 11, 2015 at 3:01

4 votes

How do I prove this field homomorphism is an isomorphism?

answered Jun 9, 2015 at 23:53

4 votes

Uniform convergence polynomial -Stone Weierstrass

answered Aug 28, 2015 at 17:01

4 votes

Prove that if the set of ideals is $\{\{0\}, R \}$, then $R$ is a field.

answered Jun 7, 2015 at 2:55

4 votes

If $f$ is a group homomorphism from $(\mathbb{Z},+)$ to $(\mathbb{Q}-\{0\},.)$ such that $f(2)=\frac{1}{3}$, then find $f(-8)$.

answered Jun 7, 2015 at 3:32

4 votes

Accepted

Prove that the splitting field of $x^{p}-q$ for prime numbers $p,q$ is an extension of degree $p(p-1)$ in $\mathbb{Q}$.

answered May 1, 2015 at 6:57

4 votes

Accepted

If Brauer characters are $\bar{\mathbb{Q}}$-linearly independent, why are they $\mathbb{C}$-linearly independent?

answered Jul 29, 2016 at 17:37

4 votes

Accepted

$K/\mathbb{Q}$ is a field extension of finite degree.Then $K\otimes_{\mathbb{Q}}K\cong K_1\oplus \cdots \oplus K_s$

answered Nov 19, 2016 at 7:20

4 votes

Definition of topological space: Is Ω equal to the powerset of X?

answered Jan 17, 2016 at 19:56

4 votes

Accepted

Cohomology of free group acting trivially

answered Jun 8, 2016 at 4:38

3 votes

Accepted

Examples of non-ideals

answered Jun 8, 2016 at 5:36

3 votes

Accepted

Showing Iterated Cosines are Equicontinuous

answered Jan 7, 2016 at 3:19

3 votes

Is there any case where a function is 1-1 where the integral=0 and the function is not odd?

answered Apr 4, 2015 at 23:05

3 votes

If $p$ is a prime number, then $\Bbb Z_{pn} \cong \Bbb Z_{p} \times \Bbb Z_{n}$ for a random integer $n$

answered Jun 6, 2015 at 17:08

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54 Answers

What is a short exact sequence?

Prove the open mapping theorem by using maximum modulus principle

Automorphism group of an infinite field.

Are these conditions sufficient for a $\mathbb{Z}$-module to be free?

Prove the set of matrices with one Jordan block is not dense in $M_n(\mathbb{C}).$

Why must a meromorphic function, bounded near infinity, have the same number of poles and zeros?

Looking for a Better Way to Think About Polynomial Rings

Is the zero ideal $\{0_{M_2(\mathbb{R})}\}$ maximal in $M_{2}(\mathbb{R})$?

Prove that there exists a real number $x$ for which $\displaystyle \sum_{k=0}^n a_kx^k = 0$

Open set containing rationals but complement non-denumerable

If $f(x,y)\in R[x,y]$ is an irreducible polynomial, is $R[x,y]/f(x,y)$ a field?

Does $f$ have a limit if $\lim_{x\to\infty}f'(x)=0$?

Continuous homorphisms between topological groups.

If a function $f$ is holomorphic on the closed unit disk centered at the origin and is real valued whenever $|z| = 1$, then $f$ is constant.

$(f(x))^p\neq f(x^p)$ on infinite field of characteristic $p$

Algebraic numbers are a field

Is this quotient of a disk Hausdorff?

How do I prove this field homomorphism is an isomorphism?

Uniform convergence polynomial -Stone Weierstrass

Prove that if the set of ideals is $\{\{0\}, R \}$, then $R$ is a field.

If $f$ is a group homomorphism from $(\mathbb{Z},+)$ to $(\mathbb{Q}-\{0\},.)$ such that $f(2)=\frac{1}{3}$, then find $f(-8)$.

Prove that the splitting field of $x^{p}-q$ for prime numbers $p,q$ is an extension of degree $p(p-1)$ in $\mathbb{Q}$.

If Brauer characters are $\bar{\mathbb{Q}}$-linearly independent, why are they $\mathbb{C}$-linearly independent?

$K/\mathbb{Q}$ is a field extension of finite degree.Then $K\otimes_{\mathbb{Q}}K\cong K_1\oplus \cdots \oplus K_s$

Definition of topological space: Is Ω equal to the powerset of X?

Cohomology of free group acting trivially

Examples of non-ideals

Showing Iterated Cosines are Equicontinuous

Is there any case where a function is 1-1 where the integral=0 and the function is not odd?

If $p$ is a prime number, then $\Bbb Z_{pn} \cong \Bbb Z_{p} \times \Bbb Z_{n}$ for a random integer $n$