Question

For a field $F$ with finite extensions $K$ and $K'$, is it true that $[KK' : F] [K\cap K':F] = [K:F][K':F]$?

score 57 · Answer 1 · 2026-04-16 07:45:53

57

Views

For a field $F$ with finite extensions $K$ and $K'$, is it true that $[KK' : F] [K\cap K':F] = [K:F][K':F]$?

Published on 16 Apr 2026 - 7:45

score 28 · Answer 2 · 2026-04-12 22:23:41

28

Views

Integral Domain

Published on 12 Apr 2026 - 22:23

score 55 · Answer 3 · 2026-04-15 21:55:34

55

Views

Field extension $\Bbb Q (\zeta_p)$

Published on 15 Apr 2026 - 21:55

score 104 · Answer 4 · 2026-04-13 21:49:36

104

Views

Construct a complete and totally ordered ﬁeld that does not have the least upper bound property.

Published on 13 Apr 2026 - 21:49

score 400 · Answer 5 · 2026-04-15 05:38:11

400

Views

Let $K$ be a finite normal extension of a field $F$. Prove that for every $\alpha \in K$, the norm of $\alpha$ over $F$ is in $F$

Published on 15 Apr 2026 - 5:38

score 421 · Answer 6 · 2026-04-14 08:08:11

421

Views

Is this proof on the insolvability of the quintic equation correct?

Published on 14 Apr 2026 - 8:08

score 82 · Answer 7 · 2026-04-16 21:59:45

82

Views

Determine the $\dim_F(Span(x_1,x_2,x_3,x_4,x_5))$ for $F=\mathbb{C},\mathbb{R},\mathbb{Q}$.

Published on 16 Apr 2026 - 21:59

score 514 · Answer 8 · 2026-04-17 02:45:08

514

Views

Does there exist a field extension of the algebraic numbers $\mathbb{A}$ other than $\mathbb{C}$?

Published on 17 Apr 2026 - 2:45

score 112 · Answer 9 · 2026-05-10 16:33:46

112

Views

Question regarding fractions of algebraic integers

Published on 10 May 2026 - 16:33

score 149 · Answer 10 · 2026-04-11 15:15:49

149

Views

Proof of Field Embedding which does not restrict identity

Published on 11 Apr 2026 - 15:15

score 754 · Answer 11 · 2026-05-10 16:34:56

754

Views

Show that algebraic integers in $\mathbb{Q}[\zeta_3]$ are exactly $\mathbb{Z}[\zeta_3]$.

Published on 10 May 2026 - 16:34

score 78 · Answer 12 · 2026-04-12 17:12:25

78

Views

Counter example to Automorphism group

Published on 12 Apr 2026 - 17:12

score 366 · Answer 13 · 2026-04-10 10:05:44

366

Views

Question about Automorphism group being isomorphic to S_n

Published on 10 Apr 2026 - 10:05

score 752 · Answer 14 · 2026-04-13 21:02:35

752

Views

Injective homomorphism between two fields of characteristic $0$ for $x\in\mathbb{Q}$

Published on 13 Apr 2026 - 21:02

score 208 · Answer 15 · 2026-04-16 11:07:41

208

Views

Is the extension $ \mathbb{Q}(\sqrt{2}, \sqrt{3}) $ simple?

Published on 16 Apr 2026 - 11:07

List Question

For a field $F$ with finite extensions $K$ and $K'$, is it true that $[KK' : F] [K\cap K':F] = [K:F][K':F]$?

Integral Domain

Field extension $\Bbb Q (\zeta_p)$

Construct a complete and totally ordered ﬁeld that does not have the least upper bound property.

Let $K$ be a finite normal extension of a field $F$. Prove that for every $\alpha \in K$, the norm of $\alpha$ over $F$ is in $F$

Is this proof on the insolvability of the quintic equation correct?

Determine the $\dim_F(Span(x_1,x_2,x_3,x_4,x_5))$ for $F=\mathbb{C},\mathbb{R},\mathbb{Q}$.

Does there exist a field extension of the algebraic numbers $\mathbb{A}$ other than $\mathbb{C}$?

Question regarding fractions of algebraic integers

Proof of Field Embedding which does not restrict identity

Show that algebraic integers in $\mathbb{Q}[\zeta_3]$ are exactly $\mathbb{Z}[\zeta_3]$.

Counter example to Automorphism group

Question about Automorphism group being isomorphic to S_n

Injective homomorphism between two fields of characteristic $0$ for $x\in\mathbb{Q}$

Is the extension $ \mathbb{Q}(\sqrt{2}, \sqrt{3}) $ simple?

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