Question

How to show that f is irreducible over Q

score 201 · Answer 1 · 2026-04-11 21:20:17

201

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How to show that f is irreducible over Q

Published on 11 Apr 2026 - 21:20

score 1.8k · Answer 2 · 2026-04-16 16:27:40

1.8k

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find total number of maximal ideals in $\mathbb{Q}[x]/\langle x^4-1\rangle$.

Published on 16 Apr 2026 - 16:27

score 53 · Answer 3 · 2026-04-15 16:03:44

53

Views

Is it true that the field $E$ which contains all $p^r$th roots of elements of a field $F$ is perfect?

Published on 15 Apr 2026 - 16:03

score 22 · Answer 4 · 2026-04-13 15:09:34

22

Views

Clarification regarding fixed elements of an automorphism

Published on 13 Apr 2026 - 15:09

score 225 · Answer 5 · 2026-04-16 00:30:37

225

Views

If there exists a monic polynomial $p(x)\in R[x]$ of degree $\geq 1$ such that the ideal $(p(x))$ is maximal, then $R$ is a field.

Published on 16 Apr 2026 - 0:30

score 1.4k · Answer 6 · 2026-04-11 13:59:47

1.4k

Views

How to factor polynomials into irreducible factors in a particular ring?

Published on 11 Apr 2026 - 13:59

score 843 · Answer 7 · 2026-04-14 21:25:30

843

Views

If α is algebraic over F then F(α) is algebraic over F

Published on 14 Apr 2026 - 21:25

score 33 · Answer 8 · 2026-04-15 00:28:59

33

Views

If $[E:K] =n$ then to prove that $|Emb_K(E,E')| \leq n$

Published on 15 Apr 2026 - 0:28

score 97 · Answer 9 · 2026-04-11 13:37:32

97

Views

Subfields of a Field

Published on 11 Apr 2026 - 13:37

score 1.3k · Answer 10 · 2026-04-16 10:19:11

1.3k

Views

Show if $\alpha$ is algebraic over $F$, then $\alpha ^2$ is algebraic over $F$

Published on 16 Apr 2026 - 10:19

score 53 · Answer 11 · 2026-04-16 20:55:09

53

Views

Proving that $\mathbb{Q}(\sqrt{p_1}) \ne \mathbb{Q}(\sqrt{p_2})$

Published on 16 Apr 2026 - 20:55

score 634 · Answer 12 · 2026-04-16 03:05:30

634

Views

Direct limit in the category of fields

Published on 16 Apr 2026 - 3:05

score 80 · Answer 13 · 2026-04-16 10:22:33

80

Views

Minimal polynomial of $\frac{\sqrt{5}+1}{2}$

Published on 16 Apr 2026 - 10:22

score 48 · Answer 14 · 2026-04-11 23:28:52

48

Views

Galois groups of a a seperable polynomial in a splitting field over $\mathbb{Q}$ and $\mathbb{Z}_p$

Published on 11 Apr 2026 - 23:28

score 603 · Answer 15 · 2026-04-15 05:33:44

603

Views

Degree of splitting field of $x^6+3x^3-2$ over $\mathbb Q$

Published on 15 Apr 2026 - 5:33

List Question

How to show that f is irreducible over Q

find total number of maximal ideals in $\mathbb{Q}[x]/\langle x^4-1\rangle$.

Is it true that the field $E$ which contains all $p^r$th roots of elements of a field $F$ is perfect?

Clarification regarding fixed elements of an automorphism

If there exists a monic polynomial $p(x)\in R[x]$ of degree $\geq 1$ such that the ideal $(p(x))$ is maximal, then $R$ is a field.

How to factor polynomials into irreducible factors in a particular ring?

If α is algebraic over F then F(α) is algebraic over F

If $[E:K] =n$ then to prove that $|Emb_K(E,E')| \leq n$

Subfields of a Field

Show if $\alpha$ is algebraic over $F$, then $\alpha ^2$ is algebraic over $F$

Proving that $\mathbb{Q}(\sqrt{p_1}) \ne \mathbb{Q}(\sqrt{p_2})$

Direct limit in the category of fields

Minimal polynomial of $\frac{\sqrt{5}+1}{2}$

Galois groups of a a seperable polynomial in a splitting field over $\mathbb{Q}$ and $\mathbb{Z}_p$

Degree of splitting field of $x^6+3x^3-2$ over $\mathbb Q$

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