Question

The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$

score 3.3k · Answer 1 · 2026-04-15 15:10:34

3.3k

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The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$

Published on 15 Apr 2026 - 15:10

score 109 · Answer 2 · 2026-04-16 06:42:34

109

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Minimal Polynomial of $1+2^{\frac{1}{n}} +\cdots+2^{\frac{n-1}{n}}$

Published on 16 Apr 2026 - 6:42

score 11.6k · Answer 3 · 2026-05-11 08:00:44

11.6k

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How can a field have a finite characteristic $p$, given that a field has no zero divisors?

Published on 11 May 2026 - 8:00

score 1k · Answer 4 · 2026-04-13 21:21:08

1k

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Example of Transcendental Extension with no Intermediate Field

Published on 13 Apr 2026 - 21:21

score 423 · Answer 5 · 2026-04-08 19:22:19

423

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Degree of Splitting Field to Prove Irreducibility

Published on 08 Apr 2026 - 19:22

score 157 · Answer 6 · 2026-04-16 06:39:00

157

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Show $ [\bar{\mathbb{Q}}:\mathbb{Q}]=\infty$

Published on 16 Apr 2026 - 6:39

score 1.7k · Answer 7 · 2026-04-16 06:57:44

1.7k

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Field of characteristic p - perfect iff pth roots of elements are all in the field.

Published on 16 Apr 2026 - 6:57

score 181 · Answer 8 · 2026-04-14 01:43:36

181

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Confused about separable elements with respect to a field

Published on 14 Apr 2026 - 1:43

score 140 · Answer 9 · 2026-04-12 05:26:53

140

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Explicit calculation of the degree of a number field extension

Published on 12 Apr 2026 - 5:26

score 207 · Answer 10 · 2026-04-16 03:30:07

207

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If $L,K$ fields, and $L(\alpha)=K(\alpha)$ then $L=K$

Published on 16 Apr 2026 - 3:30

score 461 · Answer 11 · 2026-04-16 10:41:41

461

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Subextensions of cyclotomic field

Published on 16 Apr 2026 - 10:41

score 161 · Answer 12 · 2026-04-15 21:40:18

161

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Show that $\sqrt{7}\notin\mathbb{Q}(\alpha)$, with $\alpha$ a root of $X^7+6X^3+3X+15$

Published on 15 Apr 2026 - 21:40

score 322 · Answer 13 · 2026-04-13 00:46:42

322

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Let R be the real numbers and C be the complex numbers. Can CxC be made into a field as RxR can?

Published on 13 Apr 2026 - 0:46

score 53 · Answer 14 · 2026-04-16 18:26:56

If $\sum\limits_{i=1}^{n}a_{i}^{2}=−1$. Show that if $c\in F$ $\exists$ $b_{1}, \dots , b_{k}$ of $F$ satisfying $c =\sum\limits_{i=1}^{k}b_{i}^{2}$.

score 773 · Answer 15 · 2026-05-10 19:10:23

773

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Let $F$ be a field and $f: \mathbb{Z} \to F$ be a ring epimorphism.

Published on 10 May 2026 - 19:10

List Question

The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$

Minimal Polynomial of $1+2^{\frac{1}{n}} +\cdots+2^{\frac{n-1}{n}}$

How can a field have a finite characteristic $p$, given that a field has no zero divisors?

Example of Transcendental Extension with no Intermediate Field

Degree of Splitting Field to Prove Irreducibility

Show $ [\bar{\mathbb{Q}}:\mathbb{Q}]=\infty$

Field of characteristic p - perfect iff pth roots of elements are all in the field.

Confused about separable elements with respect to a field

Explicit calculation of the degree of a number field extension

If $L,K$ fields, and $L(\alpha)=K(\alpha)$ then $L=K$

Subextensions of cyclotomic field

Show that $\sqrt{7}\notin\mathbb{Q}(\alpha)$, with $\alpha$ a root of $X^7+6X^3+3X+15$

Let R be the real numbers and C be the complex numbers. Can CxC be made into a field as RxR can?

If $\sum\limits_{i=1}^{n}a_{i}^{2}=−1$. Show that if $c\in F$ $\exists$ $b_{1}, \dots , b_{k}$ of $F$ satisfying $c =\sum\limits_{i=1}^{k}b_{i}^{2}$.

Let $F$ be a field and $f: \mathbb{Z} \to F$ be a ring epimorphism.

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