Question

Existence of certain autormorphism in Normal extensions

score 154 · Answer 1 · 2026-03-27 10:15:50

154

Views

Existence of certain autormorphism in Normal extensions

Published on 27 Mar 2026 - 10:15

score 46 · Answer 2 · 2018-10-23 17:28:35

46

Views

Is it necessary to say $x$ is an integral element of $L$?

Published on 23 Oct 2018 - 17:28

score 265 · Answer 3 · 2018-10-23 20:42:36

265

Views

Is the compositum of two finite field extensions finite?

Published on 23 Oct 2018 - 20:42

score 254 · Answer 4 · 2018-10-24 09:18:19

254

Views

Proof Compositum of Two Galois extensions is Galois. (Proof Verification)

Published on 24 Oct 2018 - 9:18

score 571 · Answer 5 · 2026-03-25 16:13:49

571

Views

Find the smallest normal extension (upto isomorphism) of $\Bbb{Q}(2^{1/4}, 3^{1/4})$ in $\overline{\Bbb{Q}}.$

Published on 25 Mar 2026 - 16:13

score 71 · Answer 6 · 2018-10-25 13:03:53

71

Views

Extension of a $F$-homomorphism where $F$ is a field.

Published on 25 Oct 2018 - 13:03

score 36 · Answer 7 · 2018-10-25 19:36:05

36

Views

Let $f(x)\in F[x]$, degree$(f(x))=n>1$, char$(F)=p$, prime and $f'(x)=0$. Prove, $p\mid n$ and $f(x)$ has at most $n/p$ distinct roots.

Published on 25 Oct 2018 - 19:36

score 100 · Answer 8 · 2018-10-25 23:15:31

100

Views

Give a direct proof that all elements of $\mathbb{Q}(\sqrt{2},\sqrt{3})$ have the form $a+b\sqrt{2}+c\sqrt{3}+d\sqrt{6}$

Published on 25 Oct 2018 - 23:15

score 164 · Answer 9 · 2026-03-25 09:10:34

164

Views

Is any rational extension of degree 3 of the form $\mathbb{Q}(\sqrt[3]{d})$?

Published on 25 Mar 2026 - 9:10

score 1.8k · Answer 10 · 2026-03-25 17:53:10

1.8k

Views

Finding the splitting field of $x^6-8$ over $\mathbb{Q}$

Published on 25 Mar 2026 - 17:53

score 60 · Answer 11 · 2026-03-25 17:52:10

60

Views

Proving irreducibiltity of $f(X)=X^3 -2 \in \mathbb{Q}[X]$ at $ \mathbb{Q}(\sqrt{2})$

Published on 25 Mar 2026 - 17:52

score 323 · Answer 12 · 2026-03-26 02:57:48

323

Views

An easy trick to compute the Galois group of a product of high degree polynomials

Published on 26 Mar 2026 - 2:57

score 68 · Answer 13 · 2026-03-27 03:00:10

68

Views

Problem regarding proving a field to be finite.

Published on 27 Mar 2026 - 3:00

score 663 · Answer 14 · 2026-03-25 15:51:50

663

Views

Let $F$ be a finite field with $p^n$ elements where char$(F)=p$

Published on 25 Mar 2026 - 15:51

score 78 · Answer 15 · 2026-03-25 15:34:28

78

Views

Structure of units in unramified extension of $\mathbb{Q}_2$

Published on 25 Mar 2026 - 15:34

List Question

Existence of certain autormorphism in Normal extensions

Is it necessary to say $x$ is an integral element of $L$?

Is the compositum of two finite field extensions finite?

Proof Compositum of Two Galois extensions is Galois. (Proof Verification)

Find the smallest normal extension (upto isomorphism) of $\Bbb{Q}(2^{1/4}, 3^{1/4})$ in $\overline{\Bbb{Q}}.$

Extension of a $F$-homomorphism where $F$ is a field.

Let $f(x)\in F[x]$, degree$(f(x))=n>1$, char$(F)=p$, prime and $f'(x)=0$. Prove, $p\mid n$ and $f(x)$ has at most $n/p$ distinct roots.

Give a direct proof that all elements of $\mathbb{Q}(\sqrt{2},\sqrt{3})$ have the form $a+b\sqrt{2}+c\sqrt{3}+d\sqrt{6}$

Is any rational extension of degree 3 of the form $\mathbb{Q}(\sqrt[3]{d})$?

Finding the splitting field of $x^6-8$ over $\mathbb{Q}$

Proving irreducibiltity of $f(X)=X^3 -2 \in \mathbb{Q}[X]$ at $ \mathbb{Q}(\sqrt{2})$

An easy trick to compute the Galois group of a product of high degree polynomials

Problem regarding proving a field to be finite.

Let $F$ be a finite field with $p^n$ elements where char$(F)=p$

Structure of units in unramified extension of $\mathbb{Q}_2$

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