Question

Proving that polynomial is irreducible over F and classifying its roots in a splitting field

score 452 · Answer 1 · 2026-03-28 15:20:17

452

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Proving that polynomial is irreducible over F and classifying its roots in a splitting field

Published on 28 Mar 2026 - 15:20

score 133 · Answer 2 · 2016-05-23 07:05:56

133

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Is $x^4 + 4$ irreducible in $\mathbb{Z}_5$?

Published on 23 May 2016 - 7:05

score 417 · Answer 3 · 2016-05-23 22:09:25

417

Views

Study of irreducibility for rings that are not integral domains.

Published on 23 May 2016 - 22:09

score 32 · Answer 4 · 2016-05-24 10:14:04

32

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Can every polynomial be moved to a irreducible one?

Published on 24 May 2016 - 10:14

score 1.1k · Answer 5 · 2016-05-25 12:03:12

1.1k

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proving that $8x^3-6x-1$ is irreducible over $\mathbb{Q}$

Published on 25 May 2016 - 12:03

score 97 · Answer 6 · 2016-05-25 18:02:23

97

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Irreducibility of polynomials in $\mathbf{Z}_p[x]$ - understanding proofs

Published on 25 May 2016 - 18:02

score 681 · Answer 7 · 2016-05-25 23:31:20

681

Views

There is no irreducible polynomial of largest degree in $\mathbf{F}_q[x]$

Published on 25 May 2016 - 23:31

score 23 · Answer 8 · 2016-05-26 00:45:57

23

Views

Moving a polynomial coefficient so it's irreducible

Published on 26 May 2016 - 0:45

score 2.6k · Answer 9 · 2016-05-29 11:25:11

2.6k

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Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$

Published on 29 May 2016 - 11:25

score 89 · Answer 10 · 2016-05-30 19:24:14

89

Views

Is there something to say about the irreducibility of polynomials and their derivatives?

Published on 30 May 2016 - 19:24

score 411 · Answer 11 · 2016-05-31 12:14:23

411

Views

Given $F \subset L \subset K$ where $K$ is a Galois ext. of $F$, find an example where $F \subset L$ is not a Galois ext.

Published on 31 May 2016 - 12:14

score 246 · Answer 12 · 2016-05-31 15:26:02

246

Views

Irreducibility Over $\def\Q{\Bbb Q}\Q[\sqrt2]$

Published on 31 May 2016 - 15:26

score 306 · Answer 13 · 2026-03-27 04:21:49

306

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Irreducibility of $X^5-7$ over $\mathbb{Q}(\sqrt[7]{2})[X]$ and degree of spitting field

Published on 27 Mar 2026 - 4:21

score 105 · Answer 14 · 2016-06-02 15:21:20

105

Views

Is $X^5+...+1 \in \mathbb{F_2}[X]$ irreducible?

Published on 02 Jun 2016 - 15:21

score 230 · Answer 15 · 2026-04-05 23:09:45

230

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Irreducible polynomial of degree $5$ in $L[X]$ using Kummer's theory

Published on 05 Apr 2026 - 23:09

List Question

Proving that polynomial is irreducible over F and classifying its roots in a splitting field

Is $x^4 + 4$ irreducible in $\mathbb{Z}_5$?

Study of irreducibility for rings that are not integral domains.

Can every polynomial be moved to a irreducible one?

proving that $8x^3-6x-1$ is irreducible over $\mathbb{Q}$

Irreducibility of polynomials in $\mathbf{Z}_p[x]$ - understanding proofs

There is no irreducible polynomial of largest degree in $\mathbf{F}_q[x]$

Moving a polynomial coefficient so it's irreducible

Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$

Is there something to say about the irreducibility of polynomials and their derivatives?

Given $F \subset L \subset K$ where $K$ is a Galois ext. of $F$, find an example where $F \subset L$ is not a Galois ext.

Irreducibility Over $\def\Q{\Bbb Q}\Q[\sqrt2]$

Irreducibility of $X^5-7$ over $\mathbb{Q}(\sqrt[7]{2})[X]$ and degree of spitting field

Is $X^5+...+1 \in \mathbb{F_2}[X]$ irreducible?

Irreducible polynomial of degree $5$ in $L[X]$ using Kummer's theory

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