Question

A finite field extension of $\mathbb R$ is either $\mathbb R$ or isomorphic to $\mathbb C$

score 4.9k · Answer 1 · 2015-03-21 14:25:21

4.9k

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A finite field extension of $\mathbb R$ is either $\mathbb R$ or isomorphic to $\mathbb C$

Published on 21 Mar 2015 - 14:25

score 22 · Answer 2 · 2015-03-24 00:49:37

22

Views

Equivalence of algebraic closures

Published on 24 Mar 2015 - 0:49

score 68 · Answer 3 · 2015-03-24 14:24:18

68

Views

Is it true that the splittings fields cannot be isomorphic?

Published on 24 Mar 2015 - 14:24

score 199 · Answer 4 · 2026-03-27 06:15:04

199

Views

(non Galois) correspondence

Published on 27 Mar 2026 - 6:15

score 654 · Answer 5 · 2015-03-25 05:17:08

654

Views

Prime ideal in the ring of integers of the number field $\mathbb{Q}(x)$ with $x^{3}=2$

Published on 25 Mar 2015 - 5:17

score 196 · Answer 6 · 2026-04-09 02:27:55

196

Views

Understanding simple transcendental field extensions

Published on 09 Apr 2026 - 2:27

score 8.6k · Answer 7 · 2026-03-27 18:56:56

8.6k

Views

Find the splitting field of $x^3-1$ over $\mathbb{Q}$.

Published on 27 Mar 2026 - 18:56

score 753 · Answer 8 · 2015-03-27 00:17:49

753

Views

How many elements does $\mathbb{Z}_2(a)$ have, where $a$ is a zero of $f(x)$ in some extension field of $\mathbb{Z}_2$

Published on 27 Mar 2015 - 0:17

score 129 · Answer 9 · 2015-03-27 00:48:43

129

Views

The field of rational functions of $k$ contains an algebraic closure of $k$?

Published on 27 Mar 2015 - 0:48

score 382 · Answer 10 · 2015-03-27 02:58:42

382

Views

Find the values of $a,b,c$ such that $(1+\sqrt[3]{4})/(2-\sqrt[3]{2})=a+b\sqrt[3]{2}+c\sqrt[3]{4}$

Published on 27 Mar 2015 - 2:58

score 5.3k · Answer 11 · 2015-03-27 03:11:01

5.3k

Views

How is the degree of the minimal polynomial related to the degree of a field extension?

Published on 27 Mar 2015 - 3:11

score 386 · Answer 12 · 2026-03-27 18:56:54

386

Views

Roots of a polynomial and finite additive subgroup

Published on 27 Mar 2026 - 18:56

score 140 · Answer 13 · 2015-03-30 03:31:15

140

Views

If $x^3 + x + 1$ is reducible over $F$, then why does it follow that $E\subseteq F$?

Published on 30 Mar 2015 - 3:31

score 94 · Answer 14 · 2026-03-27 18:56:58

94

Views

Analogue of splitting field in several variables

Published on 27 Mar 2026 - 18:56

score 209 · Answer 15 · 2015-03-30 20:46:45

209

Views

Question about $[K:F]=[K:E][E:F]$ for fields $E,F,K$

Published on 30 Mar 2015 - 20:46

List Question

A finite field extension of $\mathbb R$ is either $\mathbb R$ or isomorphic to $\mathbb C$

Equivalence of algebraic closures

Is it true that the splittings fields cannot be isomorphic?

(non Galois) correspondence

Prime ideal in the ring of integers of the number field $\mathbb{Q}(x)$ with $x^{3}=2$

Understanding simple transcendental field extensions

Find the splitting field of $x^3-1$ over $\mathbb{Q}$.

How many elements does $\mathbb{Z}_2(a)$ have, where $a$ is a zero of $f(x)$ in some extension field of $\mathbb{Z}_2$

The field of rational functions of $k$ contains an algebraic closure of $k$?

Find the values of $a,b,c$ such that $(1+\sqrt[3]{4})/(2-\sqrt[3]{2})=a+b\sqrt[3]{2}+c\sqrt[3]{4}$

How is the degree of the minimal polynomial related to the degree of a field extension?

Roots of a polynomial and finite additive subgroup

If $x^3 + x + 1$ is reducible over $F$, then why does it follow that $E\subseteq F$?

Analogue of splitting field in several variables

Question about $[K:F]=[K:E][E:F]$ for fields $E,F,K$

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