Question

Transcendence Degree of the Function Field of Meromorphic Functions over $\mathbb{C}$

score 591 · Answer 1 · 2026-03-25 17:39:19

591

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Transcendence Degree of the Function Field of Meromorphic Functions over $\mathbb{C}$

Published on 25 Mar 2026 - 17:39

score 99 · Answer 2 · 2026-04-13 06:30:45

99

Views

is $K = \mathbb{Z}[x] / (x^4+9x+6)$ a field or not?

Published on 13 Apr 2026 - 6:30

score 1.8k · Answer 3 · 2026-04-13 04:37:20

1.8k

Views

Show that it is/is not a normal extension

Published on 13 Apr 2026 - 4:37

score 198 · Answer 4 · 2026-04-16 04:30:07

198

Views

Proof or counterexample: If $F\subseteq K$ and $r\in K$. If $[F(r):F]=4$ then $F(r)=F(r^3)$.

Published on 16 Apr 2026 - 4:30

score 683 · Answer 5 · 2026-04-15 19:46:09

683

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Subfield Criteria - Proof or Counterexample

Published on 15 Apr 2026 - 19:46

score 109 · Answer 6 · 2026-04-13 19:46:55

109

Views

Dimension Field True/False.

Published on 13 Apr 2026 - 19:46

score 181 · Answer 7 · 2026-04-17 06:00:55

181

Views

If $p$ and $q$ are prime numbers and $m\gt n$ show that $\sqrt[m]{p}\notin \mathbb Q(\sqrt[n]{q})$

Published on 17 Apr 2026 - 6:00

score 138 · Answer 8 · 2026-04-15 19:33:53

138

Views

Showing $\mathbf Q(\sqrt2,\mathrm i)=\mathbf Q( \sqrt2+\mathrm i)$.

Published on 15 Apr 2026 - 19:33

score 457 · Answer 9 · 2026-04-15 00:13:44

457

Views

Each element is a square of some element

Published on 15 Apr 2026 - 0:13

score 58 · Answer 10 · 2026-04-16 11:17:20

58

Views

Let $F$ and $K$ be fields. If $F\subseteq K$ and $r\in K$ s.t. $r^2$ is algebraic over $F$. Then $r$ is algebraic over $F$.

Published on 16 Apr 2026 - 11:17

score 48 · Answer 11 · 2026-04-16 20:49:33

48

Views

Prove that $\Bbb F_p^\times$ is equal to Miller–Rabin primality test for prime number

Published on 16 Apr 2026 - 20:49

score 1.4k · Answer 12 · 2026-04-14 02:52:47

1.4k

Views

Show that an extension is separable

Published on 14 Apr 2026 - 2:52

score 143 · Answer 13 · 2026-04-15 21:07:26

143

Views

This is only a subspace if $b=0$ - Axler - LADR p13

Published on 15 Apr 2026 - 21:07

score 1.1k · Answer 14 · 2026-04-10 23:24:55

1.1k

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Galois group of a polynomial and subfields

Published on 10 Apr 2026 - 23:24

score 125 · Answer 15 · 2026-04-16 02:12:43

125

Views

Multiplicative group of a field contains maximal n-1 elements with order n

Published on 16 Apr 2026 - 2:12

List Question

Transcendence Degree of the Function Field of Meromorphic Functions over $\mathbb{C}$

is $K = \mathbb{Z}[x] / (x^4+9x+6)$ a field or not?

Show that it is/is not a normal extension

Proof or counterexample: If $F\subseteq K$ and $r\in K$. If $[F(r):F]=4$ then $F(r)=F(r^3)$.

Subfield Criteria - Proof or Counterexample

Dimension Field True/False.

If $p$ and $q$ are prime numbers and $m\gt n$ show that $\sqrt[m]{p}\notin \mathbb Q(\sqrt[n]{q})$

Showing $\mathbf Q(\sqrt2,\mathrm i)=\mathbf Q( \sqrt2+\mathrm i)$.

Each element is a square of some element

Let $F$ and $K$ be fields. If $F\subseteq K$ and $r\in K$ s.t. $r^2$ is algebraic over $F$. Then $r$ is algebraic over $F$.

Prove that $\Bbb F_p^\times$ is equal to Miller–Rabin primality test for prime number

Show that an extension is separable

This is only a subspace if $b=0$ - Axler - LADR p13

Galois group of a polynomial and subfields

Multiplicative group of a field contains maximal n-1 elements with order n

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