Question

Given a field $K$, for which separable $\alpha,\beta$ do we have $[K(\alpha,\beta):K]=[K(\alpha):K]\cdot [K(\beta):K]$?

score 80 · Answer 1 · 2026-03-25 10:55:52

80

Views

Given a field $K$, for which separable $\alpha,\beta$ do we have $[K(\alpha,\beta):K]=[K(\alpha):K]\cdot [K(\beta):K]$?

Published on 25 Mar 2026 - 10:55

score 282 · Answer 2 · 2018-04-02 14:59:07

282

Views

$Gcd(f,g)\neq 1$ implies that $f$ and $g$ have a common root in some extension of the base field

Published on 02 Apr 2018 - 14:59

score 2.3k · Answer 3 · 2026-03-25 12:13:39

2.3k

Views

Why do people study algebraic extension?

Published on 25 Mar 2026 - 12:13

score 29 · Answer 4 · 2018-04-04 14:03:47

29

Views

ring of endomorphisms of a commutative ring

Published on 04 Apr 2018 - 14:03

score 74 · Answer 5 · 2026-03-25 10:57:18

74

Views

Help finding the root of a polynomial in a field extension which adjoins the root of a separate polynomial.

Published on 25 Mar 2026 - 10:57

score 1.9k · Answer 6 · 2026-03-25 23:51:50

1.9k

Views

Minimum polynomial of a root involving the 7th root of unity

Published on 25 Mar 2026 - 23:51

score 38 · Answer 7 · 2026-03-25 04:57:03

38

Views

Quickest way to prove irreduciblity?

Published on 25 Mar 2026 - 4:57

score 30 · Answer 8 · 2026-03-25 01:23:53

30

Views

Sum of Geometric Progressions for any ordered Field

Published on 25 Mar 2026 - 1:23

score 68 · Answer 9 · 2026-03-25 22:30:15

68

Views

Verifying Isomorphism between finite fields

Published on 25 Mar 2026 - 22:30

score 53 · Answer 10 · 2018-04-05 17:07:39

53

Views

Can I construct or find out a new kind of field?

Published on 05 Apr 2018 - 17:07

score 1k · Answer 11 · 2026-03-25 12:27:22

1k

Views

Prove that the polynomial $x^4+3x+3$ is irreducible over the field $\mathbb{Q}[2^{1/3}]$

Published on 25 Mar 2026 - 12:27

score 71 · Answer 12 · 2026-03-25 12:29:25

71

Views

If $K$ and $K'$ are extensions of the same field $F$, is every isomorphism $K \to K'$ a $F$-isomorphism?

Published on 25 Mar 2026 - 12:29

score 1.1k · Answer 13 · 2026-03-25 12:24:15

1.1k

Views

Algebraic closure of $\mathbb{Q}$ in $\mathbb{C}$. Alternative proof?

Published on 25 Mar 2026 - 12:24

score 106 · Answer 14 · 2026-03-25 12:24:19

106

Views

Composite of field extensions

Published on 25 Mar 2026 - 12:24

score 293 · Answer 15 · 2026-03-25 12:24:46

293

Views

Proving the lemma $\sqrt2\notin\mathbb{Q}(\sqrt3,\sqrt5)$

Published on 25 Mar 2026 - 12:24

List Question

Given a field $K$, for which separable $\alpha,\beta$ do we have $[K(\alpha,\beta):K]=[K(\alpha):K]\cdot [K(\beta):K]$?

$Gcd(f,g)\neq 1$ implies that $f$ and $g$ have a common root in some extension of the base field

Why do people study algebraic extension?

ring of endomorphisms of a commutative ring

Help finding the root of a polynomial in a field extension which adjoins the root of a separate polynomial.

Minimum polynomial of a root involving the 7th root of unity

Quickest way to prove irreduciblity?

Sum of Geometric Progressions for any ordered Field

Verifying Isomorphism between finite fields

Can I construct or find out a new kind of field?

Prove that the polynomial $x^4+3x+3$ is irreducible over the field $\mathbb{Q}[2^{1/3}]$

If $K$ and $K'$ are extensions of the same field $F$, is every isomorphism $K \to K'$ a $F$-isomorphism?

Algebraic closure of $\mathbb{Q}$ in $\mathbb{C}$. Alternative proof?

Composite of field extensions

Proving the lemma $\sqrt2\notin\mathbb{Q}(\sqrt3,\sqrt5)$

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