User sxd

102 votes

12 answers

126k views

Good abstract algebra books for self study

asked Aug 1, 2011 at 0:32

17 votes

3 answers

3k views

Complex differentiability vs differentiability in $\mathbb{R}^2$

real-analysis complex-analysis

asked Dec 13, 2012 at 16:27

11 votes

2 answers

1k views

Question about all the homomorphisms from $\mathbb{Z}$ to $\mathbb{Z}$

abstract-algebra ring-theory self-learning

asked Aug 13, 2011 at 19:15

9 votes

2 answers

4k views

Showing that gcd does not exist for $3(1+\sqrt{-5})$ and $3(1-\sqrt{-5})$ in $\mathbb Z[\sqrt{-5}]$.

abstract-algebra number-theory divisibility

asked Feb 9, 2012 at 2:20

7 votes

3 answers

1k views

A question about prime elements in integral domains

abstract-algebra

asked Jun 26, 2011 at 1:54

4 votes

1 answer

584 views

Find all the prime ideals of $\{\frac{a}{b}| a \in \mathbb{Z}, b \in \mathbb{N}_0 \text{ odd}\}$

abstract-algebra ring-theory ideals

asked Jan 31, 2012 at 4:10

4 votes

1 answer

429 views

Open ball over the real numbers

metric-spaces

asked Oct 2, 2011 at 1:10

4 votes

1 answer

119 views

$K$ compact and $\Omega$ is open, then $\inf\{\rho(x,x') \mid x \in K \textrm{ and } x' \in \Omega^c\} > 0$

analysis metric-spaces

asked May 4, 2012 at 19:50

4 votes

1 answer

389 views

Question regarding inexpressibility results over finite models using compactness and the Löwenheim–Skolem theorem

logic model-theory

asked Apr 7, 2013 at 15:49

3 votes

2 answers

102 views

Question about a recurrence

recurrence-relations

asked Jun 14, 2012 at 16:36

3 votes

1 answer

3k views

When does a ring homomorphism preserve ideals

abstract-algebra ring-theory ideals

asked Dec 8, 2011 at 4:21

3 votes

1 answer

122 views

Question about a proof of a theorem about roots of polynomials in field extensions

abstract-algebra notation field-theory

asked Dec 14, 2011 at 1:27

3 votes

2 answers

170 views

Showing that $f: \mathbb{R} \rightarrow (-1,1): x \mapsto \frac{x}{1+|x|}$ is surjective

functions

asked Sep 30, 2011 at 10:44

2 votes

3 answers

458 views

A non zero surjective K-endomorphism is a K-automorphism

abstract-algebra field-theory

asked Dec 14, 2011 at 16:25

2 votes

2 answers

104 views

Showing that an absolute integrable monotone decreasing function $f: [1,\infty[ \rightarrow \mathbb{R}$ is in $L^p([1,\infty[)$

analysis lebesgue-integral

asked May 22, 2013 at 13:29

2 votes

2 answers

3k views

Projections in product spaces are not closed maps, false counter argument

general-topology

asked Nov 27, 2012 at 22:30

1 vote

1 answer

56 views

Continuity of $J: GL_c(E) \rightarrow GL_c(E): T \mapsto T^{-1}$

analysis normed-spaces continuity

asked Oct 28, 2012 at 0:13

1 vote

1 answer

149 views

If $B$ is a continuous bilinear function such that $B(h,k) = o(\lVert(h,k)\rVert^2)$, then $B=0$.

analysis continuity

asked Oct 29, 2012 at 23:51

1 vote

1 answer

108 views

find the Fréchet derivative of $F : [0,1] \times \mathcal{C}([0,1]) \rightarrow R : (x,f) \mapsto f(x)$, in $(x_0,f_0)$

analysis derivatives normed-spaces

asked Nov 2, 2012 at 15:28

1 vote

1 answer

371 views

Showing that a certain function is $C^1$

analysis derivatives continuity

asked Nov 15, 2012 at 17:55

1 vote

1 answer

58 views

Showing that $(\mathbb{F}_q[x]/(f_i(x)))^{F_q} = \mathbb{F}_q$

abstract-algebra field-theory

asked May 20, 2012 at 2:49

1 vote

2 answers

873 views

Question about a proof about finite normal extensions

abstract-algebra field-theory

asked Feb 15, 2012 at 23:57

0 votes

2 answers

195 views

Question about the Fréchet derivative

analysis derivatives

asked Dec 2, 2012 at 15:45

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23 Questions

Good abstract algebra books for self study

Complex differentiability vs differentiability in $\mathbb{R}^2$

Question about all the homomorphisms from $\mathbb{Z}$ to $\mathbb{Z}$

Showing that gcd does not exist for $3(1+\sqrt{-5})$ and $3(1-\sqrt{-5})$ in $\mathbb Z[\sqrt{-5}]$.

A question about prime elements in integral domains

Find all the prime ideals of $\{\frac{a}{b}| a \in \mathbb{Z}, b \in \mathbb{N}_0 \text{ odd}\}$

Open ball over the real numbers

$K$ compact and $\Omega$ is open, then $\inf\{\rho(x,x') \mid x \in K \textrm{ and } x' \in \Omega^c\} > 0$

Question regarding inexpressibility results over finite models using compactness and the Löwenheim–Skolem theorem

Question about a recurrence

When does a ring homomorphism preserve ideals

Question about a proof of a theorem about roots of polynomials in field extensions

Showing that $f: \mathbb{R} \rightarrow (-1,1): x \mapsto \frac{x}{1+|x|}$ is surjective

A non zero surjective K-endomorphism is a K-automorphism

Showing that an absolute integrable monotone decreasing function $f: [1,\infty[ \rightarrow \mathbb{R}$ is in $L^p([1,\infty[)$

Projections in product spaces are not closed maps, false counter argument

Continuity of $J: GL_c(E) \rightarrow GL_c(E): T \mapsto T^{-1}$

If $B$ is a continuous bilinear function such that $B(h,k) = o(\lVert(h,k)\rVert^2)$, then $B=0$.

find the Fréchet derivative of $F : [0,1] \times \mathcal{C}([0,1]) \rightarrow R : (x,f) \mapsto f(x)$, in $(x_0,f_0)$

Showing that a certain function is $C^1$

Showing that $(\mathbb{F}_q[x]/(f_i(x)))^{F_q} = \mathbb{F}_q$

Question about a proof about finite normal extensions

Question about the Fréchet derivative