Question

Proving $(ab)^{-1}=a^{-1}b^{-1}$ where $F$ is a field and $a,b\in F$.

score 1.3k · Answer 1 · 2026-03-30 11:04:09

1.3k

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Proving $(ab)^{-1}=a^{-1}b^{-1}$ where $F$ is a field and $a,b\in F$.

Published on 30 Mar 2026 - 11:04

score 295 · Answer 2 · 2026-04-12 15:49:12

295

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How to show rational function field of an affine subvariety with dim>0 is not algebraically closed?

Published on 12 Apr 2026 - 15:49

score 95 · Answer 3 · 2014-10-04 06:46:50

95

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For what natural numbers $n$ is $\mathbf Z/n\mathbf Z$ $[x]/(x^3+x+1)$ a field?

Published on 04 Oct 2014 - 6:46

score 155 · Answer 4 · 2014-10-04 07:16:08

155

Views

Proving if $a$ and $b$ are positive rational numbers and $\mathbb Q(\sqrt{a})=\mathbb Q(\sqrt{b})$ then $b=ac^2$ for some $c\in \mathbb Q$.

Published on 04 Oct 2014 - 7:16

score 1.1k · Answer 5 · 2026-04-11 16:31:46

1.1k

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Compute the transcendence degree (transcendence degree and tensor products)

Published on 11 Apr 2026 - 16:31

score 87 · Answer 6 · 2014-10-04 08:59:50

87

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Proof/Counterexample: If $z$ is a complex number and $z\notin \mathbb Q$, then $\mathbb Q(z)=\mathbb Q(z^3,z^5)$.

Published on 04 Oct 2014 - 8:59

score 1.9k · Answer 7 · 2026-04-13 04:07:35

1.9k

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Proof that a given set is a field

Published on 13 Apr 2026 - 4:07

score 12k · Answer 8 · 2026-04-10 17:13:58

12k

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Homomorphisms between fields are injective.

Published on 10 Apr 2026 - 17:13

score 72 · Answer 9 · 2026-04-12 22:13:36

72

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Algebraic element

Published on 12 Apr 2026 - 22:13

score 1.5k · Answer 10 · 2026-04-12 00:05:13

1.5k

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Galois group of reducible polynomial

Published on 12 Apr 2026 - 0:05

score 149 · Answer 11 · 2026-04-10 23:55:41

149

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proof using field axioms only

Published on 10 Apr 2026 - 23:55

score 47 · Answer 12 · 2014-10-06 20:18:05

47

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Write it as an element of this ring?

Published on 06 Oct 2014 - 20:18

score 2.7k · Answer 13 · 2026-04-12 03:55:51

2.7k

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How to check field axioms given addition and multiplication tables

Published on 12 Apr 2026 - 3:55

score 54 · Answer 14 · 2014-10-06 23:23:18

When $0$ is mentioned at anytime when talking about Fields, does this mean we are talking about the number $0$, or is it the additive identity?

score 71 · Answer 15 · 2026-04-10 06:55:48

71

Views

Field extension-Why does this hold?

Published on 10 Apr 2026 - 6:55

List Question

Proving $(ab)^{-1}=a^{-1}b^{-1}$ where $F$ is a field and $a,b\in F$.

How to show rational function field of an affine subvariety with dim>0 is not algebraically closed?

For what natural numbers $n$ is $\mathbf Z/n\mathbf Z$ $[x]/(x^3+x+1)$ a field?

Proving if $a$ and $b$ are positive rational numbers and $\mathbb Q(\sqrt{a})=\mathbb Q(\sqrt{b})$ then $b=ac^2$ for some $c\in \mathbb Q$.

Compute the transcendence degree (transcendence degree and tensor products)

Proof/Counterexample: If $z$ is a complex number and $z\notin \mathbb Q$, then $\mathbb Q(z)=\mathbb Q(z^3,z^5)$.

Proof that a given set is a field

Homomorphisms between fields are injective.

Algebraic element

Galois group of reducible polynomial

proof using field axioms only

Write it as an element of this ring?

How to check field axioms given addition and multiplication tables

When $0$ is mentioned at anytime when talking about Fields, does this mean we are talking about the number $0$, or is it the additive identity?

Field extension-Why does this hold?

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