Question

Write down the $8$ elements of $ F_2[x]/(x^3 + x + 1) $ in terms of α

score 758 · Answer 1 · 2026-03-28 17:41:17

758

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Write down the $8$ elements of $ F_2[x]/(x^3 + x + 1) $ in terms of α

Published on 28 Mar 2026 - 17:41

score 227 · Answer 2 · 2019-04-09 01:09:12

227

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Is there always a way to generate nontrivial finite extensions of a field?

Published on 09 Apr 2019 - 1:09

score 487 · Answer 3 · 2026-03-28 15:59:37

487

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Proving the ideal generated by subset of a ring is the set of linear combinations of the subset and the ring.

Published on 28 Mar 2026 - 15:59

score 568 · Answer 4 · 2026-04-01 00:25:26

568

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$\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})=\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ for $p_{1},p_{2}$ primes.

Published on 01 Apr 2026 - 0:25

score 93 · Answer 5 · 2019-04-10 15:28:15

Let $ \alpha=2^{1/5} $ and $\zeta=e^{2i\pi/5} $ and let $K=\mathbb{Q}(\alpha\zeta) $ then how many field automorphism of $K $ have?

score 64 · Answer 6 · 2026-03-27 23:14:15

Let $\alpha=2^{1/5}$ ,$\zeta=e^{2i\pi/5}$ and $K=\mathbb{Q}(\alpha\zeta)$, can the field automorphism of K be extended to an automorphism of C?

score 129 · Answer 7 · 2026-04-01 02:01:55

129

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"Some examples of the Galois correspondence" lecture notes of K.Conrad

Published on 01 Apr 2026 - 2:01

score 59 · Answer 8 · 2026-03-28 15:55:30

59

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Why is $GF(p^n)$ unique?

Published on 28 Mar 2026 - 15:55

score 133 · Answer 9 · 2026-04-01 02:03:28

133

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Extension $\mathbb{Q}(\sqrt[3]{2},\sqrt[3]{3})$ over $\mathbb{Q}$ and its degree

Published on 01 Apr 2026 - 2:03

score 273 · Answer 10 · 2026-03-28 00:48:40

273

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What is $l$-th division polynomial of $E$?

Published on 28 Mar 2026 - 0:48

score 166 · Answer 11 · 2019-04-12 16:21:37

166

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Why $\mathbb Q[\sqrt 2]$ is a field?

Published on 12 Apr 2019 - 16:21

score 39 · Answer 12 · 2026-03-26 13:07:37

39

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Notation for this quaternary linear code

Published on 26 Mar 2026 - 13:07

score 60 · Answer 13 · 2026-03-31 13:10:03

60

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A question regarding finding the minimal polynomial associated with a field extension .

Published on 31 Mar 2026 - 13:10

score 204 · Answer 14 · 2026-03-25 11:16:51

204

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Is there a procedure to calculate the multiplicative inverse in a quotient by a maximal ideal?

Published on 25 Mar 2026 - 11:16

score 471 · Answer 15 · 2026-03-25 03:03:41

471

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Number of n-tuples in $\{0, 1, 2\}$ with sum less than or equal to $d$.

Published on 25 Mar 2026 - 3:03

List Question

Write down the $8$ elements of $ F_2[x]/(x^3 + x + 1) $ in terms of α

Is there always a way to generate nontrivial finite extensions of a field?

Proving the ideal generated by subset of a ring is the set of linear combinations of the subset and the ring.

$\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})=\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ for $p_{1},p_{2}$ primes.

Let $ \alpha=2^{1/5} $ and $\zeta=e^{2i\pi/5} $ and let $K=\mathbb{Q}(\alpha\zeta) $ then how many field automorphism of $K $ have?

Let $\alpha=2^{1/5}$ ,$\zeta=e^{2i\pi/5}$ and $K=\mathbb{Q}(\alpha\zeta)$, can the field automorphism of K be extended to an automorphism of C?

"Some examples of the Galois correspondence" lecture notes of K.Conrad

Why is $GF(p^n)$ unique?

Extension $\mathbb{Q}(\sqrt[3]{2},\sqrt[3]{3})$ over $\mathbb{Q}$ and its degree

What is $l$-th division polynomial of $E$?

Why $\mathbb Q[\sqrt 2]$ is a field?

Notation for this quaternary linear code

A question regarding finding the minimal polynomial associated with a field extension .

Is there a procedure to calculate the multiplicative inverse in a quotient by a maximal ideal?

Number of n-tuples in $\{0, 1, 2\}$ with sum less than or equal to $d$.

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