Question

Norm and Trace of an element is an integer, then element is an integral?

score 1.6k · Answer 1 · 2026-04-08 21:59:17

Norm and Trace of an element is an integer, then element is an integral?

Published on 08 Apr 2026 - 21:59

score 105 · Answer 2 · 2026-04-17 09:33:10

Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.

score 42 · Answer 3 · 2026-04-12 23:48:44

42

Views

Proving that $[k[u]:k[u^l]]=1$ if $(l,[k[u]:k])=1$

Published on 12 Apr 2026 - 23:48

score 151 · Answer 4 · 2026-04-15 16:46:26

151

Views

Let $F$ be a field in which we have elements satisfying $a^2+b^2+c^2 = −1$. Show that there exist elements satisfying $d^2+e^2 = −1$.

Published on 15 Apr 2026 - 16:46

score 94 · Answer 5 · 2026-04-16 01:37:43

94

Views

Let $F$ be a field and let $a,b,c,d\in F\Rightarrow (a^2+b^2)(c^2+d^2)$ can be written as $x^2+y^2$ for some $x,y\in F$?

Published on 16 Apr 2026 - 1:37

score 549 · Answer 6 · 2026-04-10 18:18:56

549

Views

Is $\mathbb{R}$ an algebraic extension of some proper subfield?

Published on 10 Apr 2026 - 18:18

score 50 · Answer 7 · 2026-04-15 04:46:38

50

Views

$L:K$ is algebraic implies that $\bar{L}=\bar{K}$?

Published on 15 Apr 2026 - 4:46

score 18.4k · Answer 8 · 2026-04-11 12:28:02

18.4k

Views

How to find the degree of a field extension

Published on 11 Apr 2026 - 12:28

score 2.3k · Answer 9 · 2026-04-15 21:59:27

2.3k

Views

Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.

Published on 15 Apr 2026 - 21:59

score 151 · Answer 10 · 2026-04-10 12:22:11

151

Views

Is the compositum morally equivalent to the sum?

Published on 10 Apr 2026 - 12:22

score 331 · Answer 11 · 2026-04-17 13:50:28

331

Views

$F$ a field and $G$ finite subset of $F \setminus \{0\}$ with 1 & satisfying $a, b ∈ G$ then $ab^{−1} ∈ G$. Show that $G$ is cyclic

Published on 17 Apr 2026 - 13:50

score 230 · Answer 12 · 2026-04-16 11:39:15

230

Views

Showing $x^{p^e}-a$ is irreducible in imperfect field of characteristic p

Published on 16 Apr 2026 - 11:39

score 88 · Answer 13 · 2026-04-14 01:19:05

88

Views

Expressing a number field in a simpler way

Published on 14 Apr 2026 - 1:19

score 305 · Answer 14 · 2026-04-17 15:08:02

305

Views

$[F(\alpha+\beta):F(\beta)]=[F(\alpha):F(\beta)]$?

Published on 17 Apr 2026 - 15:08

score 83 · Answer 15 · 2026-04-12 23:25:11

83

Views

About $K$-embeddings and the pertinence of an element of a finite and separable field extension

Published on 12 Apr 2026 - 23:25

List Question

Norm and Trace of an element is an integer, then element is an integral?

Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.

Proving that $[k[u]:k[u^l]]=1$ if $(l,[k[u]:k])=1$

Let $F$ be a field in which we have elements satisfying $a^2+b^2+c^2 = −1$. Show that there exist elements satisfying $d^2+e^2 = −1$.

Let $F$ be a field and let $a,b,c,d\in F\Rightarrow (a^2+b^2)(c^2+d^2)$ can be written as $x^2+y^2$ for some $x,y\in F$?

Is $\mathbb{R}$ an algebraic extension of some proper subfield?

$L:K$ is algebraic implies that $\bar{L}=\bar{K}$?

How to find the degree of a field extension

Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.

Is the compositum morally equivalent to the sum?

$F$ a field and $G$ finite subset of $F \setminus \{0\}$ with 1 & satisfying $a, b ∈ G$ then $ab^{−1} ∈ G$. Show that $G$ is cyclic

Showing $x^{p^e}-a$ is irreducible in imperfect field of characteristic p

Expressing a number field in a simpler way

$[F(\alpha+\beta):F(\beta)]=[F(\alpha):F(\beta)]$?

About $K$-embeddings and the pertinence of an element of a finite and separable field extension

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