Question

How do I find _all_ the roots of $f$ in $F_{27}$ hence show that $f$ splits in $F_{27}$

score 116 · Answer 1 · 2026-04-15 06:53:13

116

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How do I find _all_ the roots of $f$ in $F_{27}$ hence show that $f$ splits in $F_{27}$

Published on 15 Apr 2026 - 6:53

score 40 · Answer 2 · 2026-04-16 21:36:43

40

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If $F\subseteq K \subseteq J \subseteq L$, then $[L:F]=[F:K][K:J][J:L]$?

Published on 16 Apr 2026 - 21:36

score 71 · Answer 3 · 2026-04-14 22:10:52

71

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$R$ - commutative ring. $I$ - ideal of that ring. Prove that ring $R/I$ - is a field

Published on 14 Apr 2026 - 22:10

score 122 · Answer 4 · 2026-04-04 20:25:59

122

Views

$L/K$ field extension, $\alpha\in\overline{K}$, does $\deg f_L^\alpha \mid \deg f_K^\alpha$?

Published on 04 Apr 2026 - 20:25

score 92 · Answer 5 · 2026-04-16 19:53:25

92

Views

Degree of splitting field is either $1$ or $2$

Published on 16 Apr 2026 - 19:53

score 884 · Answer 6 · 2026-04-16 15:35:07

884

Views

$E_1/F$ and $E_2/F$ finite field extensions, does degree of compositum $E_1E_2$ over $F$ divide the product $[E_1:F] [E_2:F]$?

Published on 16 Apr 2026 - 15:35

score 594 · Answer 7 · 2026-04-09 13:36:59

594

Views

Degree of separability equals degree of separable closure

Published on 09 Apr 2026 - 13:36

score 253 · Answer 8 · 2026-04-15 09:07:52

253

Views

Why is char $K \ne 2$ needed in this proof by Artin and Schreier that shows a field is algebraically closed?

Published on 15 Apr 2026 - 9:07

score 584 · Answer 9 · 2026-04-16 06:05:04

584

Views

Show $\sqrt[3]{5}$ is not contained in any cyclotomic extension of $\mathbb{Q}$.

Published on 16 Apr 2026 - 6:05

score 107 · Answer 10 · 2026-04-13 14:02:52

107

Views

Examples of Galois Groups that are Algebraic Groups

Published on 13 Apr 2026 - 14:02

score 112 · Answer 11 · 2026-04-11 09:30:47

112

Views

Field extension of degree three

Published on 11 Apr 2026 - 9:30

score 927 · Answer 12 · 2026-04-15 04:31:51

927

Views

Prove$(2,x^2+x+1)$ is a maximal ideal of $\mathbb{Z}[x]$

Published on 15 Apr 2026 - 4:31

score 94 · Answer 13 · 2026-03-25 09:53:52

94

Views

Difficulty in building a Galois-equivariant map in the cyclotomic case

Published on 25 Mar 2026 - 9:53

score 41 · Answer 14 · 2026-04-16 22:58:17

41

Views

Solve $\mathbb{Q}$[X] /$\mathbb{Q}$[X]($X^3$+$X$) $\cong$ $\mathbb{Q}$ x $\mathbb{Q}$[X]/($X^2$ $+$ $1$)

Published on 16 Apr 2026 - 22:58

score 65 · Answer 15 · 2026-04-15 18:04:30

65

Views

The Fields of Fractions Induced by Two Similar, but Distinct Integral Domains

Published on 15 Apr 2026 - 18:04

List Question

How do I find _all_ the roots of $f$ in $F_{27}$ hence show that $f$ splits in $F_{27}$

If $F\subseteq K \subseteq J \subseteq L$, then $[L:F]=[F:K][K:J][J:L]$?

$R$ - commutative ring. $I$ - ideal of that ring. Prove that ring $R/I$ - is a field

$L/K$ field extension, $\alpha\in\overline{K}$, does $\deg f_L^\alpha \mid \deg f_K^\alpha$?

Degree of splitting field is either $1$ or $2$

$E_1/F$ and $E_2/F$ finite field extensions, does degree of compositum $E_1E_2$ over $F$ divide the product $[E_1:F] [E_2:F]$?

Degree of separability equals degree of separable closure

Why is char $K \ne 2$ needed in this proof by Artin and Schreier that shows a field is algebraically closed?

Show $\sqrt[3]{5}$ is not contained in any cyclotomic extension of $\mathbb{Q}$.

Examples of Galois Groups that are Algebraic Groups

Field extension of degree three

Prove$(2,x^2+x+1)$ is a maximal ideal of $\mathbb{Z}[x]$

Difficulty in building a Galois-equivariant map in the cyclotomic case

Solve $\mathbb{Q}$[X] /$\mathbb{Q}$[X]($X^3$+$X$) $\cong$ $\mathbb{Q}$ x $\mathbb{Q}$[X]/($X^2$ $+$ $1$)

The Fields of Fractions Induced by Two Similar, but Distinct Integral Domains

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