Question

Simple way to prove that $\mathbb{Z}[\sqrt[3]{2}]=\mathcal{O}_{\mathbb{Q}(\sqrt[3]{2})}$

score 396 · Answer 1 · 2026-04-15 21:46:25

396

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Simple way to prove that $\mathbb{Z}[\sqrt[3]{2}]=\mathcal{O}_{\mathbb{Q}(\sqrt[3]{2})}$

Published on 15 Apr 2026 - 21:46

score 199 · Answer 2 · 2026-04-05 00:37:30

199

Views

Simplify $\mathbb{Q}(\pi^3+\pi^2, \pi^8+\pi^5)$

Published on 05 Apr 2026 - 0:37

score 240 · Answer 3 · 2026-04-14 12:35:03

240

Views

$\mathbb{F}_{16}$ does not contain a subfield of order 8

Published on 14 Apr 2026 - 12:35

score 118 · Answer 4 · 2026-04-11 12:58:55

118

Views

Finite field extension proposition - need explanation

Published on 11 Apr 2026 - 12:58

score 537 · Answer 5 · 2026-04-11 05:19:40

537

Views

Is $\Bbb C$ a purely transcendental extension of a proper subfield?

Published on 11 Apr 2026 - 5:19

score 201 · Answer 6 · 2026-04-09 06:40:33

201

Views

Torsion-free, divisible multiplicative groups of fields

Published on 09 Apr 2026 - 6:40

score 3.5k · Answer 7 · 2026-04-16 16:05:01

3.5k

Views

Find the polynomials which satisfy the condition $f(x)\mid f(x^2)$

Published on 16 Apr 2026 - 16:05

score 650 · Answer 8 · 2026-04-16 14:34:26

650

Views

Find the number of distinct linearly dependent sets of the form $\{u,v\}$

Published on 16 Apr 2026 - 14:34

score 68 · Answer 9 · 2026-04-10 14:04:09

68

Views

What is $\mathbb Z[t]/(t,5)$?

Published on 10 Apr 2026 - 14:04

score 90 · Answer 10 · 2026-04-16 04:26:25

90

Views

Find a polynomial with roots which are functions of roots of an irreducible polynomial

Published on 16 Apr 2026 - 4:26

score 96 · Answer 11 · 2026-04-12 20:12:45

96

Views

Can the complex numbers be totally ordered and how is this different to $\mathbb{C}$ being an ordered field?

Published on 12 Apr 2026 - 20:12

score 451 · Answer 12 · 2026-04-16 12:21:09

451

Views

Is the set of smooth functions from R to R both a vector space and a ring?

Published on 16 Apr 2026 - 12:21

score 601 · Answer 13 · 2026-04-14 09:37:27

601

Views

Cardinality of infinite transcendence bases

Published on 14 Apr 2026 - 9:37

score 434 · Answer 14 · 2026-04-13 01:06:17

434

Views

Transcendental element and algebraic closure

Published on 13 Apr 2026 - 1:06

score 44 · Answer 15 · 2026-04-12 09:56:45

44

Views

What is meant by $F(\beta )$ in field theory?

Published on 12 Apr 2026 - 9:56

List Question

Simple way to prove that $\mathbb{Z}[\sqrt[3]{2}]=\mathcal{O}_{\mathbb{Q}(\sqrt[3]{2})}$

Simplify $\mathbb{Q}(\pi^3+\pi^2, \pi^8+\pi^5)$

$\mathbb{F}_{16}$ does not contain a subfield of order 8

Finite field extension proposition - need explanation

Is $\Bbb C$ a purely transcendental extension of a proper subfield?

Torsion-free, divisible multiplicative groups of fields

Find the polynomials which satisfy the condition $f(x)\mid f(x^2)$

Find the number of distinct linearly dependent sets of the form $\{u,v\}$

What is $\mathbb Z[t]/(t,5)$?

Find a polynomial with roots which are functions of roots of an irreducible polynomial

Can the complex numbers be totally ordered and how is this different to $\mathbb{C}$ being an ordered field?

Is the set of smooth functions from R to R both a vector space and a ring?

Cardinality of infinite transcendence bases

Transcendental element and algebraic closure

What is meant by $F(\beta )$ in field theory?

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