Question

Prove that $[\mathbb{Q}(\sqrt{3},i):\mathbb{Q}=4$. Find a number $a$, such that $\mathbb{Q}(a)=\mathbb{Q}(\sqrt{3},i)$

score 109 · Answer 1 · 2026-04-01 06:09:06

109

Views

Prove that $[\mathbb{Q}(\sqrt{3},i):\mathbb{Q}=4$. Find a number $a$, such that $\mathbb{Q}(a)=\mathbb{Q}(\sqrt{3},i)$

Published on 01 Apr 2026 - 6:09

score 86 · Answer 2 · 2026-04-02 07:21:52

86

Views

Galois group of order $n!$

Published on 02 Apr 2026 - 7:21

score 86 · Answer 3 · 2026-04-08 02:06:22

86

Views

Proof Explanation Field and Galois Theory

Published on 08 Apr 2026 - 2:06

score 382 · Answer 4 · 2019-08-17 19:09:22

382

Views

Show that $\sqrt[3]{1+\sqrt{3}}$ isn't an element of the field $\mathbb{Q}(\sqrt{3} ,\sqrt[3]{2})$

Published on 17 Aug 2019 - 19:09

score 208 · Answer 5 · 2026-04-04 13:50:51

208

Views

Elements of $E^{\times},\cdot$ of the quotient ring $E:= \frac{\mathbb{Z}_3[X]}{\langle x^2 + x + 2\rangle}$

Published on 04 Apr 2026 - 13:50

score 305 · Answer 6 · 2026-04-02 07:23:21

305

Views

Galois Group of $\mathbb{Q}(\sqrt{\sqrt{3}-1})$

Published on 02 Apr 2026 - 7:23

score 222 · Answer 7 · 2026-04-01 06:06:15

222

Views

Is there an algebraic closed field which contains the complex field $\mathbb{C}$ strictly?

Published on 01 Apr 2026 - 6:06

score 160 · Answer 8 · 2026-04-01 06:11:15

160

Views

Show that $\mathbb{Q}(\sin\theta)$ is a field

Published on 01 Apr 2026 - 6:11

score 36 · Answer 9 · 2026-03-26 01:26:59

36

Views

Question about finite extensions and splitting fields

Published on 26 Mar 2026 - 1:26

score 49 · Answer 10 · 2026-03-29 19:17:35

49

Views

Why $X$ is a primitive r-th root of unity in lemma 4.7 Prime is in P?

Published on 29 Mar 2026 - 19:17

score 36 · Answer 11 · 2019-08-19 15:01:05

36

Views

In ZFC there exists a perfect field of given positive characteristic and given infinite cardinality

Published on 19 Aug 2019 - 15:01

score 96 · Answer 12 · 2026-03-25 10:59:04

96

Views

$S$ is a commutative integral domain and a finitely generated $R$-Module where $R$ is a subring of $S$. $R$ is a field iff $S$ is a field

Published on 25 Mar 2026 - 10:59

score 264 · Answer 13 · 2019-08-20 08:41:21

264

Views

There does not exist a onto ring homomorphism from $M_{n+1 \times n+1}(\mathbb F) \to M_{n \times n}(\mathbb F) $ for any field $\mathbb F.$

Published on 20 Aug 2019 - 8:41

score 1k · Answer 14 · 2019-08-21 20:19:24

1k

Views

Place at infinity in function fields

Published on 21 Aug 2019 - 20:19

score 219 · Answer 15 · 2026-03-31 22:08:05

219

Views

If $R$ is a ring, $K$ a field (and subring of $R$), and $I$ a proper ideal of $R$, $R/I$ contains a field isomorphic to $K$

Published on 31 Mar 2026 - 22:08

List Question

Prove that $[\mathbb{Q}(\sqrt{3},i):\mathbb{Q}=4$. Find a number $a$, such that $\mathbb{Q}(a)=\mathbb{Q}(\sqrt{3},i)$

Galois group of order $n!$

Proof Explanation Field and Galois Theory

Show that $\sqrt[3]{1+\sqrt{3}}$ isn't an element of the field $\mathbb{Q}(\sqrt{3} ,\sqrt[3]{2})$

Elements of $E^{\times},\cdot$ of the quotient ring $E:= \frac{\mathbb{Z}_3[X]}{\langle x^2 + x + 2\rangle}$

Galois Group of $\mathbb{Q}(\sqrt{\sqrt{3}-1})$

Is there an algebraic closed field which contains the complex field $\mathbb{C}$ strictly?

Show that $\mathbb{Q}(\sin\theta)$ is a field

Question about finite extensions and splitting fields

Why $X$ is a primitive r-th root of unity in lemma 4.7 Prime is in P?

In ZFC there exists a perfect field of given positive characteristic and given infinite cardinality

$S$ is a commutative integral domain and a finitely generated $R$-Module where $R$ is a subring of $S$. $R$ is a field iff $S$ is a field

There does not exist a onto ring homomorphism from $M_{n+1 \times n+1}(\mathbb F) \to M_{n \times n}(\mathbb F) $ for any field $\mathbb F.$

Place at infinity in function fields

If $R$ is a ring, $K$ a field (and subring of $R$), and $I$ a proper ideal of $R$, $R/I$ contains a field isomorphic to $K$

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