Question

Degree of sum of algebraic elements

score 282 · Answer 1 · 2026-04-13 05:40:29

282

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Degree of sum of algebraic elements

Published on 13 Apr 2026 - 5:40

score 1.4k · Answer 2 · 2026-04-16 20:00:12

1.4k

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Prove that $\mathbb{Q}(\alpha) = \mathbb{Q}(\alpha^{2})$

Published on 16 Apr 2026 - 20:00

score 87 · Answer 3 · 2026-04-14 23:50:22

87

Views

rational roots of a cubic

Published on 14 Apr 2026 - 23:50

score 156 · Answer 4 · 2026-04-14 02:11:31

156

Views

A problem in extension fields

Published on 14 Apr 2026 - 2:11

score 35 · Answer 5 · 2026-04-18 10:29:49

35

Views

Finding the smallest $k$ such that $f(x)$ divides $1-x^k$ where $f(x)$ is over $\mbox{GF}(2)$?

Published on 18 Apr 2026 - 10:29

score 40 · Answer 6 · 2026-04-10 22:49:17

40

Views

a question on spliting field

Published on 10 Apr 2026 - 22:49

score 1.9k · Answer 7 · 2026-04-17 03:56:40

1.9k

Views

Find the degree and a basis for $\mathbb{Q}( \sqrt2, \sqrt3)$ over $ \mathbb{Q}( \sqrt2 +\sqrt 3)$

Published on 17 Apr 2026 - 3:56

score 410 · Answer 8 · 2026-04-13 21:49:11

410

Views

Regular matrix and field extension.

Published on 13 Apr 2026 - 21:49

score 49 · Answer 9 · 2026-04-15 06:11:28

49

Views

show that the extension $\mathbb{Z}_{2}(X)\supseteq \mathbb{Z}_{2}(X^2+X)$ is Galois

Published on 15 Apr 2026 - 6:11

score 1.2k · Answer 10 · 2026-04-17 01:40:47

1.2k

Views

Tensor product of algebraic closure with an algebraic extension of a field

Published on 17 Apr 2026 - 1:40

score 67 · Answer 11 · 2026-04-14 16:05:57

67

Views

Simultaneous irreducibility of minimal polynomials

Published on 14 Apr 2026 - 16:05

score 310 · Answer 12 · 2026-04-14 12:53:34

310

Views

Perfect field of characteristic $p>0$ which is not an algebraic extension of the prime field

Published on 14 Apr 2026 - 12:53

score 1.1k · Answer 13 · 2026-04-17 09:57:02

1.1k

Views

Find Galois group and all intermediate fields of the extension $L=\mathbb{Q}(\sqrt[4]{2},i)\supseteq \mathbb{Q}=K$

Published on 17 Apr 2026 - 9:57

score 58 · Answer 14 · 2026-04-18 15:20:11

58

Views

Why is it true that $F_{q^n} = F_q(\alpha)$ where $\alpha$ is the primitive element of $F_{q^n}$?

Published on 18 Apr 2026 - 15:20

score 78 · Answer 15 · 2026-04-18 15:20:11

78

Views

If $\alpha$ = $\beta^q - \beta$ where both $\alpha$ , $\beta $ belongs to $F_q^n$ which is extension of $F_q$

Published on 18 Apr 2026 - 15:20

List Question

Degree of sum of algebraic elements

Prove that $\mathbb{Q}(\alpha) = \mathbb{Q}(\alpha^{2})$

rational roots of a cubic

A problem in extension fields

Finding the smallest $k$ such that $f(x)$ divides $1-x^k$ where $f(x)$ is over $\mbox{GF}(2)$?

a question on spliting field

Find the degree and a basis for $\mathbb{Q}( \sqrt2, \sqrt3)$ over $ \mathbb{Q}( \sqrt2 +\sqrt 3)$

Regular matrix and field extension.

show that the extension $\mathbb{Z}_{2}(X)\supseteq \mathbb{Z}_{2}(X^2+X)$ is Galois

Tensor product of algebraic closure with an algebraic extension of a field

Simultaneous irreducibility of minimal polynomials

Perfect field of characteristic $p>0$ which is not an algebraic extension of the prime field

Find Galois group and all intermediate fields of the extension $L=\mathbb{Q}(\sqrt[4]{2},i)\supseteq \mathbb{Q}=K$

Why is it true that $F_{q^n} = F_q(\alpha)$ where $\alpha$ is the primitive element of $F_{q^n}$?

If $\alpha$ = $\beta^q - \beta$ where both $\alpha$ , $\beta $ belongs to $F_q^n$ which is extension of $F_q$

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