Question

Embedded primes in a finitely generated algebra over an algebraically closed field

score 77 · Answer 1 · 2026-03-18 19:57:30

77

Views

Embedded primes in a finitely generated algebra over an algebraically closed field

Published on 18 Mar 2026 - 19:57

score 85 · Answer 2 · 2026-03-28 02:22:09

85

Views

Linearity of the map Field Trace.

Published on 28 Mar 2026 - 2:22

score 590 · Answer 3 · 2026-03-30 17:15:36

590

Views

The minimal polynomial satisfied by the primitive generator

Published on 30 Mar 2026 - 17:15

score 892 · Answer 4 · 2026-03-27 18:08:12

892

Views

Normal Subgroup of Galois Group

Published on 27 Mar 2026 - 18:08

score 78 · Answer 5 · 2019-01-27 12:39:29

78

Views

Prove that $t^4 + t^3 + t^2 + t+1$ is not a primitive polynomial for $\mathbb{F}_2$

Published on 27 Jan 2019 - 12:39

score 78 · Answer 6 · 2019-01-27 17:04:09

78

Views

Deductions using Field axioms

Published on 27 Jan 2019 - 17:04

score 307 · Answer 7 · 2026-03-25 13:58:11

307

Views

For $c\in\mathbb{F}_p^*$, the cubic $t^3-3ct^2-3t+c$ has exactly one root $r\in\mathbb{F}_p$. Express $r$ in terms of $c$ without cubic roots.

Published on 25 Mar 2026 - 13:58

score 59 · Answer 8 · 2026-03-30 11:15:09

59

Views

Extended field for $u^2+1$

Published on 30 Mar 2026 - 11:15

score 169 · Answer 9 · 2026-03-26 13:51:38

169

Views

irreducibility of polynomial over field of rational functions

Published on 26 Mar 2026 - 13:51

score 64 · Answer 10 · 2019-01-29 19:50:35

Prove that each element in a finite field with characteristic $p$ is a $p$-th power for exactly one element in that field.

score 39 · Answer 11 · 2026-03-25 07:48:49

39

Views

What elements does a map of rings fix if both rings contain the same algebraically closed field as a subring?

Published on 25 Mar 2026 - 7:48

score 944 · Answer 12 · 2026-03-25 21:01:33

944

Views

Prove that $[ \mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}]=8.$

Published on 25 Mar 2026 - 21:01

score 169 · Answer 13 · 2026-02-23 01:23:03

169

Views

Is it true that $Gal(K/F)\cong S_{n_1}\times \cdots S_{n_k}$?

Published on 23 Feb 2026 - 1:23

score 392 · Answer 14 · 2026-02-23 01:25:37

392

Views

$x^2-3$ is separable over $\mathbb Q$ but not separable over $F_2$

Published on 23 Feb 2026 - 1:25

score 48 · Answer 15 · 2019-01-30 00:49:08

48

Views

How many products can a $K$-vector space have?

Published on 30 Jan 2019 - 0:49

List Question

Embedded primes in a finitely generated algebra over an algebraically closed field

Linearity of the map Field Trace.

The minimal polynomial satisfied by the primitive generator

Normal Subgroup of Galois Group

Prove that $t^4 + t^3 + t^2 + t+1$ is not a primitive polynomial for $\mathbb{F}_2$

Deductions using Field axioms

For $c\in\mathbb{F}_p^*$, the cubic $t^3-3ct^2-3t+c$ has exactly one root $r\in\mathbb{F}_p$. Express $r$ in terms of $c$ without cubic roots.

Extended field for $u^2+1$

irreducibility of polynomial over field of rational functions

Prove that each element in a finite field with characteristic $p$ is a $p$-th power for exactly one element in that field.

What elements does a map of rings fix if both rings contain the same algebraically closed field as a subring?

Prove that $[ \mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}]=8.$

Is it true that $Gal(K/F)\cong S_{n_1}\times \cdots S_{n_k}$?

$x^2-3$ is separable over $\mathbb Q$ but not separable over $F_2$

How many products can a $K$-vector space have?

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