Question

Minimal polynomial of $\varphi:g+(f)\mapsto xg+(f)$ is $f$.

score 54 · Answer 1 · 2026-04-17 05:14:45

54

Views

Minimal polynomial of $\varphi:g+(f)\mapsto xg+(f)$ is $f$.

Published on 17 Apr 2026 - 5:14

score 288 · Answer 2 · 2026-04-14 16:35:52

288

Views

How can I prove $f=x^n-a \in F[X]$ is separable?

Published on 14 Apr 2026 - 16:35

score 93 · Answer 3 · 2026-04-15 17:57:25

93

Views

Feedback is needed: Describe the Galois group of the polynomial $x^5 -3 ∈ \mathbb{Q}(\zeta)[x]$ over $\mathbb{Q}(\zeta)$.

Published on 15 Apr 2026 - 17:57

score 35 · Answer 4 · 2026-04-11 16:56:51

35

Views

Upper bound on polynomial over a field

Published on 11 Apr 2026 - 16:56

score 2.4k · Answer 5 · 2026-04-15 10:44:03

2.4k

Views

Meaning of "extension field is a vector space"

Published on 15 Apr 2026 - 10:44

score 1.1k · Answer 6 · 2026-04-13 14:41:58

1.1k

Views

Basis of ring of algebraic integers and free modules

Published on 13 Apr 2026 - 14:41

score 136 · Answer 7 · 2026-04-17 11:47:18

136

Views

Number of elements $a\in\mathbb{F}_{5^4}$ such that $\mathbb{F}_{5^4}=\mathbb{F}_5(a)$

Published on 17 Apr 2026 - 11:47

score 388 · Answer 8 · 2026-04-15 23:24:08

388

Views

If $\text{Gal}(K/\mathbb{Q})\cong Z_5$, then show $K(\sqrt{2})/\mathbb{Q}$ is Galois

Published on 15 Apr 2026 - 23:24

score 78 · Answer 9 · 2026-04-11 08:37:39

78

Views

Field norm well-behaved with respect to minimal polynomial

Published on 11 Apr 2026 - 8:37

score 147 · Answer 10 · 2026-04-09 20:44:31

147

Views

Finding irreducible polynomial in finite field

Published on 09 Apr 2026 - 20:44

score 193 · Answer 11 · 2026-04-15 17:46:36

193

Views

How to find the degree of the extension $[\mathbb{Q}(\sqrt[4]{3+2\sqrt{5}}):\mathbb{Q}]$?

Published on 15 Apr 2026 - 17:46

score 90 · Answer 12 · 2026-04-11 19:02:58

90

Views

Is $\mathbb{Q}(\sqrt{pq})$ a subfield of $\mathbb{R}$?

Published on 11 Apr 2026 - 19:02

score 42 · Answer 13 · 2026-03-25 11:32:59

42

Views

$K(\zeta)/k(\zeta)$ is Galois (proof verification)

Published on 25 Mar 2026 - 11:32

score 205 · Answer 14 · 2026-04-14 23:39:48

205

Views

Let F be a field of characteristic p and let $\alpha \in F$ be an element for which $f(\alpha)=0$. Prove that $f(\alpha^p)=0$

Published on 14 Apr 2026 - 23:39

score 393 · Answer 15 · 2026-03-25 16:01:36

393

Views

Algebraic Extensions of Z_7 with polynomials?

Published on 25 Mar 2026 - 16:01

List Question

Minimal polynomial of $\varphi:g+(f)\mapsto xg+(f)$ is $f$.

How can I prove $f=x^n-a \in F[X]$ is separable?

Feedback is needed: Describe the Galois group of the polynomial $x^5 -3 ∈ \mathbb{Q}(\zeta)[x]$ over $\mathbb{Q}(\zeta)$.

Upper bound on polynomial over a field

Meaning of "extension field is a vector space"

Basis of ring of algebraic integers and free modules

Number of elements $a\in\mathbb{F}_{5^4}$ such that $\mathbb{F}_{5^4}=\mathbb{F}_5(a)$

If $\text{Gal}(K/\mathbb{Q})\cong Z_5$, then show $K(\sqrt{2})/\mathbb{Q}$ is Galois

Field norm well-behaved with respect to minimal polynomial

Finding irreducible polynomial in finite field

How to find the degree of the extension $[\mathbb{Q}(\sqrt[4]{3+2\sqrt{5}}):\mathbb{Q}]$?

Is $\mathbb{Q}(\sqrt{pq})$ a subfield of $\mathbb{R}$?

$K(\zeta)/k(\zeta)$ is Galois (proof verification)

Let F be a field of characteristic p and let $\alpha \in F$ be an element for which $f(\alpha)=0$. Prove that $f(\alpha^p)=0$

Algebraic Extensions of Z_7 with polynomials?

Trending Questions

Popular # Hahtags

Popular Questions