Question

an "explicit" extension field that contains a root of an irreducible polynomial

score 232 · Answer 1 · 2015-04-06 03:42:07

232

Views

an "explicit" extension field that contains a root of an irreducible polynomial

Published on 06 Apr 2015 - 3:42

score 121 · Answer 2 · 2026-04-09 08:26:35

121

Views

Normal extension and action of automorphisms on factors

Published on 09 Apr 2026 - 8:26

score 34 · Answer 3 · 2015-04-08 15:44:36

34

Views

prove n divides $[\mathbb{F}[\alpha]:\mathbb{Q}]$

Published on 08 Apr 2015 - 15:44

score 161 · Answer 4 · 2015-04-09 00:49:04

161

Views

If $I$ proper ideal of $R$, $S$ ring extension of $R$, and $u$ a unit in $S$, then $IR[u] \ne R[u]$ or $IR[u^{−1}] \ne R[u^{-1}]$

Published on 09 Apr 2015 - 0:49

score 97 · Answer 5 · 2026-04-07 14:38:28

97

Views

Extensions of fields and dimension

Published on 07 Apr 2026 - 14:38

score 48 · Answer 6 · 2015-04-09 18:53:56

48

Views

Why are ring extensions only discussed in the context of $\mathbb{C}$?

Published on 09 Apr 2015 - 18:53

score 215 · Answer 7 · 2015-04-10 10:48:55

215

Views

Rigorously prove $\mathbb{Q}(\sqrt2,\sqrt3) = \mathbb{Q}(\sqrt2) (\sqrt3)$

Published on 10 Apr 2015 - 10:48

score 1.2k · Answer 8 · 2015-04-11 16:26:27

1.2k

Views

Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.

Published on 11 Apr 2015 - 16:26

score 143 · Answer 9 · 2015-04-12 21:24:38

143

Views

$i \notin \mathbb{Q}[\sqrt[4]{2}]$ without using topological properties of $\mathbb{R}$

Published on 12 Apr 2015 - 21:24

score 171 · Answer 10 · 2015-04-13 05:56:41

171

Views

The discriminant of (1,x,x^2) in a cubic field.

Published on 13 Apr 2015 - 5:56

score 125 · Answer 11 · 2015-04-13 18:47:21

125

Views

Finding degree of minimal polynomial of $a$ over $F$

Published on 13 Apr 2015 - 18:47

score 100 · Answer 12 · 2015-04-13 22:43:16

100

Views

Degree of extension fields

Published on 13 Apr 2015 - 22:43

score 58 · Answer 13 · 2026-04-11 05:59:32

58

Views

Degree of minimal polynomial over $\mathbb{Z}_7$

Published on 11 Apr 2026 - 5:59

score 111 · Answer 14 · 2026-04-03 00:23:05

111

Views

Extend ${\bigl(1+\frac1x\bigr)}^{{x}}$ to $\overline{\mathbb R}$

Published on 03 Apr 2026 - 0:23

score 506 · Answer 15 · 2026-04-10 18:01:32

506

Views

Finite field extension over the rationals need only one generator?

Published on 10 Apr 2026 - 18:01

List Question

an "explicit" extension field that contains a root of an irreducible polynomial

Normal extension and action of automorphisms on factors

prove n divides $[\mathbb{F}[\alpha]:\mathbb{Q}]$

If $I$ proper ideal of $R$, $S$ ring extension of $R$, and $u$ a unit in $S$, then $IR[u] \ne R[u]$ or $IR[u^{−1}] \ne R[u^{-1}]$

Extensions of fields and dimension

Why are ring extensions only discussed in the context of $\mathbb{C}$?

Rigorously prove $\mathbb{Q}(\sqrt2,\sqrt3) = \mathbb{Q}(\sqrt2) (\sqrt3)$

Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.

$i \notin \mathbb{Q}[\sqrt[4]{2}]$ without using topological properties of $\mathbb{R}$

The discriminant of (1,x,x^2) in a cubic field.

Finding degree of minimal polynomial of $a$ over $F$

Degree of extension fields

Degree of minimal polynomial over $\mathbb{Z}_7$

Extend ${\bigl(1+\frac1x\bigr)}^{{x}}$ to $\overline{\mathbb R}$

Finite field extension over the rationals need only one generator?

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