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sxd
  • Member for 11 years
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102 votes
12 answers
126k views

Good abstract algebra books for self study

17 votes
3 answers
3k views

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

11 votes
2 answers
1k views

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

9 votes
2 answers
4k views

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

7 votes
3 answers
1k views

A question about prime elements in integral domains

4 votes
1 answer
584 views

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

4 votes
1 answer
429 views

Open ball over the real numbers

4 votes
1 answer
119 views

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

4 votes
1 answer
389 views

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

3 votes
2 answers
102 views

Question about a recurrence

3 votes
1 answer
3k views

When does a ring homomorphism preserve ideals

3 votes
1 answer
122 views

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

3 votes
2 answers
170 views

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

2 votes
3 answers
458 views

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

2 votes
2 answers
104 views

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

2 votes
2 answers
3k views

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

1 vote
1 answer
56 views

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

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 $B=0$.

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 $(x_0,f_0)$

1 vote
1 answer
371 views

Showing that a certain function is $C^1$

1 vote
1 answer
58 views

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

1 vote
2 answers
873 views

Question about a proof about finite normal extensions

0 votes
2 answers
195 views

Question about the Fréchet derivative