Question

Characterizing all primitive elements of a simple extension

score 52 · Answer 1 · 2024-01-18 12:59:35

52

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Characterizing all primitive elements of a simple extension

Published on 18 Jan 2024 - 12:59

score 66 · Answer 2 · 2026-03-27 15:36:07

66

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Irreducibility of $f$, automorphisms $\sigma \in \text{Aut}_{\mathbb Q}(L)$

Published on 27 Mar 2026 - 15:36

score 41 · Answer 3 · 2024-01-19 00:34:57

41

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Linear equations in field extension

Published on 19 Jan 2024 - 0:34

score 31 · Answer 4 · 2024-01-20 11:13:23

31

Views

$\bar{x}$ notation in Field Theory

Published on 20 Jan 2024 - 11:13

score 87 · Answer 5 · 2024-01-22 09:06:31

87

Views

Regarding the isomorphism $PGL(2,K) \cong GL(2,K)/Scal(2, K)$ and a degree of a field extension

Published on 22 Jan 2024 - 9:06

score 29 · Answer 6 · 2026-04-03 23:04:44

29

Views

"Galois group" acts transitively on irreducible factors in the context of normal extensions (not necessarily separable)

Published on 03 Apr 2026 - 23:04

score 74 · Answer 7 · 2026-04-06 18:45:13

74

Views

Finite extension of finite field

Published on 06 Apr 2026 - 18:45

score 83 · Answer 8 · 2024-01-30 17:11:20

83

Views

Factorization of ideals in number fields of the form $K=\mathbb{Q}(\alpha,\beta)$

Published on 30 Jan 2024 - 17:11

score 35 · Answer 9 · 2026-03-25 17:20:02

35

Views

the degree of the discriminant of a cubic irreducibble polynomial over the rational adjoint a root

Published on 25 Mar 2026 - 17:20

score 46 · Answer 10 · 2024-02-02 20:16:10

Show $\mathrm{disc}(1,\alpha,\dots,\alpha^{d-1})=(-1)^{d(d-1)/2}N_{\mathbb Q(\alpha)/\mathbb Q}(f'(\alpha))$, with $d=[\mathbb Q(\alpha):\mathbb Q]$

score 144 · Answer 11 · 2026-04-03 23:02:23

144

Views

Is there an algorithm to check if a polynomial with integer coefficients is reducible over some extension of $\mathbb Q$?

Published on 03 Apr 2026 - 23:02

score 31 · Answer 12 · 2026-03-28 10:41:36

31

Views

Every ring $R$ with $K ⊆ R ⊆ L$ (subrings) is a field $\Leftrightarrow$ $L/K$ is algebraic

Published on 28 Mar 2026 - 10:41

score 45 · Answer 13 · 2024-02-05 14:20:13

45

Views

$L/K$ field extension and $[M : K] ≤ C$ holds for all real intermediate fields $M$. Then $[L : K]$ is also finite

Published on 05 Feb 2024 - 14:20

score 32 · Answer 14 · 2026-04-04 00:48:22

32

Views

Show degree of minimal polynomial has to be even

Published on 04 Apr 2026 - 0:48

score 43 · Answer 15 · 2026-04-01 08:04:48

43

Views

Extending the Fundamental Theorem of Projective Geometry to projective lines over quadratic field extensions

Published on 01 Apr 2026 - 8:04

List Question

Characterizing all primitive elements of a simple extension

Irreducibility of $f$, automorphisms $\sigma \in \text{Aut}_{\mathbb Q}(L)$

Linear equations in field extension

$\bar{x}$ notation in Field Theory

Regarding the isomorphism $PGL(2,K) \cong GL(2,K)/Scal(2, K)$ and a degree of a field extension

"Galois group" acts transitively on irreducible factors in the context of normal extensions (not necessarily separable)

Finite extension of finite field

Factorization of ideals in number fields of the form $K=\mathbb{Q}(\alpha,\beta)$

the degree of the discriminant of a cubic irreducibble polynomial over the rational adjoint a root

Show $\mathrm{disc}(1,\alpha,\dots,\alpha^{d-1})=(-1)^{d(d-1)/2}N_{\mathbb Q(\alpha)/\mathbb Q}(f'(\alpha))$, with $d=[\mathbb Q(\alpha):\mathbb Q]$

Is there an algorithm to check if a polynomial with integer coefficients is reducible over some extension of $\mathbb Q$?

Every ring $R$ with $K ⊆ R ⊆ L$ (subrings) is a field $\Leftrightarrow$ $L/K$ is algebraic

$L/K$ field extension and $[M : K] ≤ C$ holds for all real intermediate fields $M$. Then $[L : K]$ is also finite

Show degree of minimal polynomial has to be even

Extending the Fundamental Theorem of Projective Geometry to projective lines over quadratic field extensions

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