Question

Minimal polynomial is invariant under field extensions

score 1.7k · Answer 1 · 2026-04-13 19:40:26

1.7k

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Minimal polynomial is invariant under field extensions

Published on 13 Apr 2026 - 19:40

score 504 · Answer 2 · 2026-04-13 12:51:03

504

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A sufficient condition for irreducibility of a polynomial in an extension field.

Published on 13 Apr 2026 - 12:51

score 942 · Answer 3 · 2026-04-13 14:04:09

942

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How to show field extension equality

Published on 13 Apr 2026 - 14:04

score 414 · Answer 4 · 2026-04-16 15:42:15

414

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Number rings and (round) parentheses versus (square) brackets

Published on 16 Apr 2026 - 15:42

score 264 · Answer 5 · 2026-04-12 02:31:45

264

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Determine the degree of another field extension.

Published on 12 Apr 2026 - 2:31

score 1.5k · Answer 6 · 2026-04-12 05:39:17

1.5k

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Finite extensions of fields that are algebraically closed

Published on 12 Apr 2026 - 5:39

score 146 · Answer 7 · 2026-04-16 16:59:08

146

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Abstract Algebra: Field extensions

Published on 16 Apr 2026 - 16:59

score 59 · Answer 8 · 2026-04-13 18:20:46

59

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is the field extension $\mathbb{Z}_{3}(X)\supseteq \mathbb{Z}_{3}(X^2)$ normal

Published on 13 Apr 2026 - 18:20

score 1.4k · Answer 9 · 2026-04-16 23:14:04

1.4k

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Conjugate isomorphism of the automorphism groups of two field extensions?

Published on 16 Apr 2026 - 23:14

score 1.1k · Answer 10 · 2026-04-11 06:09:32

1.1k

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Difference between Galois extension and separable extension

Published on 11 Apr 2026 - 6:09

score 706 · Answer 11 · 2026-04-18 10:30:16

706

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Irreducible polynomial f in polynomial ring of finite field order n divides a particular polynomial if and only if degree of f divides n

Published on 18 Apr 2026 - 10:30

score 78 · Answer 12 · 2026-04-15 22:28:14

78

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Find fixed field of K-automorphisms of $L:=\mathbb{R}(X,Y)$

Published on 15 Apr 2026 - 22:28

score 83 · Answer 13 · 2026-04-17 13:15:01

83

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Why is $K(\alpha) = \left\lbrace \frac{f(\alpha)}{g(\alpha)} : f,g\in K[X],\, g(\alpha)\neq 0\right\rbrace$?

Published on 17 Apr 2026 - 13:15

score 1.6k · Answer 14 · 2026-04-16 07:44:29

1.6k

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Finding the minimal polynomial in this field extension of $\mathbb Q$?

Published on 16 Apr 2026 - 7:44

score 556 · Answer 15 · 2026-04-15 19:27:51

556

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minimal field extension of Q($\sqrt[3] {2}$)

Published on 15 Apr 2026 - 19:27

List Question

Minimal polynomial is invariant under field extensions

A sufficient condition for irreducibility of a polynomial in an extension field.

How to show field extension equality

Number rings and (round) parentheses versus (square) brackets

Determine the degree of another field extension.

Finite extensions of fields that are algebraically closed

Abstract Algebra: Field extensions

is the field extension $\mathbb{Z}_{3}(X)\supseteq \mathbb{Z}_{3}(X^2)$ normal

Conjugate isomorphism of the automorphism groups of two field extensions?

Difference between Galois extension and separable extension

Irreducible polynomial f in polynomial ring of finite field order n divides a particular polynomial if and only if degree of f divides n

Find fixed field of K-automorphisms of $L:=\mathbb{R}(X,Y)$

Why is $K(\alpha) = \left\lbrace \frac{f(\alpha)}{g(\alpha)} : f,g\in K[X],\, g(\alpha)\neq 0\right\rbrace$?

Finding the minimal polynomial in this field extension of $\mathbb Q$?

minimal field extension of Q($\sqrt[3] {2}$)

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