Question

Proving that $K\otimes_{\mathbb{Q}}\mathbb{C}\simeq \prod_{\tau}\mathbb{C}$

score 222 · Answer 1 · 2026-04-16 00:50:01

222

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Proving that $K\otimes_{\mathbb{Q}}\mathbb{C}\simeq \prod_{\tau}\mathbb{C}$

Published on 16 Apr 2026 - 0:50

score 107 · Answer 2 · 2026-04-16 06:33:17

107

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Determine whether or not there is an automorphism $\sigma \in Gal(M/F)$ with $\sigma (a) = a'$ and $\sigma(b) = b'$.

Published on 16 Apr 2026 - 6:33

score 202 · Answer 3 · 2026-04-14 01:36:01

202

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$k$ is algebraically closed in $K$, and $lK=L$ , but $l$ is not algebraically closed in $L$.

Published on 14 Apr 2026 - 1:36

score 271 · Answer 4 · 2026-04-16 21:45:15

271

Views

$[K : F]_s = [K : L]_s [L : F]_s $ and $[K : F]_i = [K : L]_i [L : F]_i $

Published on 16 Apr 2026 - 21:45

score 65 · Answer 5 · 2026-04-15 07:33:24

65

Views

$\{\sigma(\alpha)|\sigma \in U\}$ is finite.

Published on 15 Apr 2026 - 7:33

score 51 · Answer 6 · 2026-04-15 06:36:31

51

Views

For all elements $x$ in any Archimedean ordered field, there is a $q \in \mathbb Q:q<x$

Published on 15 Apr 2026 - 6:36

score 250 · Answer 7 · 2026-04-15 16:49:48

250

Views

Reduced product isomorphic to $\mathbb{C}$

Published on 15 Apr 2026 - 16:49

score 52 · Answer 8 · 2026-04-13 02:03:58

52

Views

Existance of an invertible matrix.

Published on 13 Apr 2026 - 2:03

score 150 · Answer 9 · 2026-04-10 01:20:35

150

Views

Degree of a finite field extension. How to find?

Published on 10 Apr 2026 - 1:20

score 50 · Answer 10 · 2026-04-18 12:20:41

50

Views

For any element of Archimedean ordered field there is a greater natural number

Published on 18 Apr 2026 - 12:20

score 72 · Answer 11 · 2026-04-12 20:34:48

72

Views

$Z = \{x \in K \mid \sigma_1(x) = \cdots = \sigma_n(x)\}$ is a subfield of K with $[K : Z] \geq n$.

Published on 12 Apr 2026 - 20:34

score 1.1k · Answer 12 · 2026-04-14 23:10:45

1.1k

Views

Why Krull dimension of $k[x,y,z]/(xy-z^2)$ is 2?

Published on 14 Apr 2026 - 23:10

score 55 · Answer 13 · 2026-04-15 20:06:09

55

Views

IF $a^m=b^n=1$ show $c^k=1$, $k$ least common multiple of m and n

Published on 15 Apr 2026 - 20:06

score 48 · Answer 14 · 2026-04-17 05:13:24

48

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$m_a(x) = x^n + b_1x^{n−1} + \cdots + b_n$ be the minimal polynomial of $a$ over $E$. Prove that $E = K(b_1, \ldots , b_n)$

Published on 17 Apr 2026 - 5:13

score 1k · Answer 15 · 2026-04-11 15:15:53

1k

Views

Proof of Hilbert's nullstellensatz,

Published on 11 Apr 2026 - 15:15

List Question

Proving that $K\otimes_{\mathbb{Q}}\mathbb{C}\simeq \prod_{\tau}\mathbb{C}$

Determine whether or not there is an automorphism $\sigma \in Gal(M/F)$ with $\sigma (a) = a'$ and $\sigma(b) = b'$.

$k$ is algebraically closed in $K$, and $lK=L$ , but $l$ is not algebraically closed in $L$.

$[K : F]_s = [K : L]_s [L : F]_s $ and $[K : F]_i = [K : L]_i [L : F]_i $

$\{\sigma(\alpha)|\sigma \in U\}$ is finite.

For all elements $x$ in any Archimedean ordered field, there is a $q \in \mathbb Q:q<x$

Reduced product isomorphic to $\mathbb{C}$

Existance of an invertible matrix.

Degree of a finite field extension. How to find?

For any element of Archimedean ordered field there is a greater natural number

$Z = \{x \in K \mid \sigma_1(x) = \cdots = \sigma_n(x)\}$ is a subfield of K with $[K : Z] \geq n$.

Why Krull dimension of $k[x,y,z]/(xy-z^2)$ is 2?

IF $a^m=b^n=1$ show $c^k=1$, $k$ least common multiple of m and n

$m_a(x) = x^n + b_1x^{n−1} + \cdots + b_n$ be the minimal polynomial of $a$ over $E$. Prove that $E = K(b_1, \ldots , b_n)$

Proof of Hilbert's nullstellensatz,

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