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Confusion regarding proof of a proposition in Field Theory (Dumb Question)

score 125 · Answer 1 · 2026-04-10 02:10:27

125

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Confusion regarding proof of a proposition in Field Theory (Dumb Question)

Published on 10 Apr 2026 - 2:10

score 870 · Answer 2 · 2026-03-30 00:22:46

870

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Prove that $(a+b\sqrt[3]{2}+c\sqrt[3]{4})^{-1}$ with a,b,c∈Q is a number of the form $d+e\sqrt[3]{2}+f\sqrt[3]{4}$ with $d,e,f∈Q$

Published on 30 Mar 2026 - 0:22

score 70 · Answer 3 · 2026-04-04 02:24:03

70

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Isomorphic algebraic closures.

Published on 04 Apr 2026 - 2:24

score 67 · Answer 4 · 2026-04-12 06:09:10

67

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For which values of $a\in\mathbb ℤ/3\mathbb ℤ$ is the quotient $\mathbb ℤ/3\mathbb ℤ[x]/(x^3+x^2+ax+1)$ a field?

Published on 12 Apr 2026 - 6:09

score 177 · Answer 5 · 2014-08-05 17:56:31

177

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Is there a ring $K$ such that $\mathbb R\subsetneqq K\subsetneqq \mathbb C$?

Published on 05 Aug 2014 - 17:56

score 63 · Answer 6 · 2026-04-12 16:40:01

63

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Places of this extension

Published on 12 Apr 2026 - 16:40

score 2.2k · Answer 7 · 2026-04-12 04:09:49

2.2k

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Minimal polynomial for $\zeta+\zeta^5$ for a primitive seventh root of unity $\zeta$

Published on 12 Apr 2026 - 4:09

score 132 · Answer 8 · 2014-08-06 18:05:33

132

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Let $F$ be a field and let $f(x)$ be a non constant element of $F[x]$. Then, there exists a splitting field $E$ for $f(x)$ over $F$.

Published on 06 Aug 2014 - 18:05

score 1.3k · Answer 9 · 2026-04-11 15:16:59

1.3k

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Discrete valuations of the rational numbers

Published on 11 Apr 2026 - 15:16

score 478 · Answer 10 · 2026-04-12 03:17:34

478

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Are order isomorphic real closed fields isomorphic?

Published on 12 Apr 2026 - 3:17

score 231 · Answer 11 · 2026-04-02 05:29:18

231

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Zeroes of f(x) in a splitting field $E $ have the same multiplicity

Published on 02 Apr 2026 - 5:29

score 754 · Answer 12 · 2026-04-11 00:16:31

754

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Every field with characterisitic $p$ contains the field $\mathbb{Z}_p$

Published on 11 Apr 2026 - 0:16

score 4.6k · Answer 13 · 2026-04-02 05:20:53

4.6k

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Describe the elements in $\mathbb{Q}(\pi)$

Published on 02 Apr 2026 - 5:20

score 106 · Answer 14 · 2026-04-12 15:33:24

106

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How do elements of $\mathbb{R}(xy,x+y)$ look like?

Published on 12 Apr 2026 - 15:33

score 950 · Answer 15 · 2026-03-27 06:17:16

950

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Quadratic number fields containing primitive roots of unity

Published on 27 Mar 2026 - 6:17

List Question

Confusion regarding proof of a proposition in Field Theory (Dumb Question)

Prove that $(a+b\sqrt[3]{2}+c\sqrt[3]{4})^{-1}$ with a,b,c∈Q is a number of the form $d+e\sqrt[3]{2}+f\sqrt[3]{4}$ with $d,e,f∈Q$

Isomorphic algebraic closures.

For which values of $a\in\mathbb ℤ/3\mathbb ℤ$ is the quotient $\mathbb ℤ/3\mathbb ℤ[x]/(x^3+x^2+ax+1)$ a field?

Is there a ring $K$ such that $\mathbb R\subsetneqq K\subsetneqq \mathbb C$?

Places of this extension

Minimal polynomial for $\zeta+\zeta^5$ for a primitive seventh root of unity $\zeta$

Let $F$ be a field and let $f(x)$ be a non constant element of $F[x]$. Then, there exists a splitting field $E$ for $f(x)$ over $F$.

Discrete valuations of the rational numbers

Are order isomorphic real closed fields isomorphic?

Zeroes of f(x) in a splitting field $E $ have the same multiplicity

Every field with characterisitic $p$ contains the field $\mathbb{Z}_p$

Describe the elements in $\mathbb{Q}(\pi)$

How do elements of $\mathbb{R}(xy,x+y)$ look like?

Quadratic number fields containing primitive roots of unity

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