Question

Minimal extension of $\mathbb{Q}$ such that a polynomial split into conjugate factors

score 37 · Answer 1 · 2026-04-25 02:32:44

37

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Minimal extension of $\mathbb{Q}$ such that a polynomial split into conjugate factors

Published on 25 Apr 2026 - 2:32

score 108 · Answer 2 · 2026-04-17 01:50:37

108

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Why $[\mathbb{F}_{p}(\alpha): \mathbb{F}_{p^n}] = p$?

Published on 17 Apr 2026 - 1:50

score 31 · Answer 3 · 2026-05-15 15:10:04

31

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Primitive element of a finite field whose powers do not lie inside the prime subfield

Published on 15 May 2026 - 15:10

score 44 · Answer 4 · 2026-04-16 09:24:42

44

Views

Determening the field of invariants of some automorphisms of $\mathbb{Q}(x)$

Published on 16 Apr 2026 - 9:24

score 24 · Answer 5 · 2026-04-09 21:19:41

24

Views

Proof of a telescoping formula for separable degrees in Hungerford's Algebra.

Published on 09 Apr 2026 - 21:19

score 35 · Answer 6 · 2026-04-13 04:06:48

35

Views

Explicit Upper Bound for Class Number of Quadratic Field

Published on 13 Apr 2026 - 4:06

score 51 · Answer 7 · 2026-04-13 05:15:09

51

Views

Is the converse of $\bmod p$ method in determining Galois group true? Or is there a prime corresponding to every member of the Galois group?

Published on 13 Apr 2026 - 5:15

score 29 · Answer 8 · 2026-04-12 10:41:32

29

Views

Question about finite extensions

Published on 12 Apr 2026 - 10:41

score 87 · Answer 9 · 2026-04-10 16:13:19

87

Views

Question on two isomorphic simple algebraic extension

Published on 10 Apr 2026 - 16:13

score 49 · Answer 10 · 2026-04-13 09:30:45

49

Views

Polynomial for each extension degree

Published on 13 Apr 2026 - 9:30

score 498 · Answer 11 · 2026-04-10 13:12:02

498

Views

Must algebraic extensions of the same degree have subfields of the same degree?

Published on 10 Apr 2026 - 13:12

score 105 · Answer 12 · 2026-04-14 10:18:36

105

Views

Why can't this happen in fields $K$ with $\operatorname{char}(K)=0$?

Published on 14 Apr 2026 - 10:18

score 107 · Answer 13 · 2026-04-12 15:30:47

107

Views

Specific question on imaginary quadratic field

Published on 12 Apr 2026 - 15:30

score 312 · Answer 14 · 2026-04-13 20:00:09

312

Views

Algebraic closure of the rational inside a quotient of product of finite fields

Published on 13 Apr 2026 - 20:00

score 1.2k · Answer 15 · 2026-04-14 01:00:52

1.2k

Views

Show the quotient ring R/I is not a field

Published on 14 Apr 2026 - 1:00

List Question

Minimal extension of $\mathbb{Q}$ such that a polynomial split into conjugate factors

Why $[\mathbb{F}_{p}(\alpha): \mathbb{F}_{p^n}] = p$?

Primitive element of a finite field whose powers do not lie inside the prime subfield

Determening the field of invariants of some automorphisms of $\mathbb{Q}(x)$

Proof of a telescoping formula for separable degrees in Hungerford's Algebra.

Explicit Upper Bound for Class Number of Quadratic Field

Is the converse of $\bmod p$ method in determining Galois group true? Or is there a prime corresponding to every member of the Galois group?

Question about finite extensions

Question on two isomorphic simple algebraic extension

Polynomial for each extension degree

Must algebraic extensions of the same degree have subfields of the same degree?

Why can't this happen in fields $K$ with $\operatorname{char}(K)=0$?

Specific question on imaginary quadratic field

Algebraic closure of the rational inside a quotient of product of finite fields

Show the quotient ring R/I is not a field

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