Question

Describe $\mathbb{R}[x]/(x^{2}+ax+b)$ where $a,b \in \mathbb{R}$

score 182 · Answer 1 · 2026-03-25 17:37:56

182

Views

Describe $\mathbb{R}[x]/(x^{2}+ax+b)$ where $a,b \in \mathbb{R}$

Published on 25 Mar 2026 - 17:37

score 42 · Answer 2 · 2026-03-29 08:15:14

42

Views

Normal closure of a field extension adjoined by a $3$-rd root of unity

Published on 29 Mar 2026 - 8:15

score 383 · Answer 3 · 2026-03-25 17:37:48

383

Views

Does there exist irreducible polynomials of each degree over arbitrary field?

Published on 25 Mar 2026 - 17:37

score 309 · Answer 4 · 2026-03-25 06:18:52

309

Views

Proving multiplication is compatible with ordering considering an ordered field.

Published on 25 Mar 2026 - 6:18

score 26 · Answer 5 · 2018-08-26 22:34:17

Proving that $[F(x_1 , x_2) : F] = p_1 p_2$, where $p_1 = \deg \min(x_1 , F)$ and $p_2 = \deg \min(x_2 , F)$ are coprime.

score 53 · Answer 6 · 2026-03-31 19:16:48

53

Views

About field of fractions and their classification in the case of $K\left(\eta\right)$

Published on 31 Mar 2026 - 19:16

score 433 · Answer 7 · 2026-03-31 19:14:59

433

Views

Elementary proof of $\mathcal{O}_K$ is a free abelian group of rank $n$

Published on 31 Mar 2026 - 19:14

score 202 · Answer 8 · 2026-03-25 12:16:28

202

Views

Is uncountable transcendental-additions enough to make $\mathbb{Q}$ into $\mathbb{R}$?

Published on 25 Mar 2026 - 12:16

score 29 · Answer 9 · 2018-08-28 23:38:58

29

Views

A simple question about normal closure of field extensions.

Published on 28 Aug 2018 - 23:38

score 303 · Answer 10 · 2026-03-29 12:05:42

303

Views

Proving that this polynomial has no roots in this field

Published on 29 Mar 2026 - 12:05

score 217 · Answer 11 · 2026-03-29 08:18:21

217

Views

Is there a field extension that causes polynomials to factor, but not into linear factors?

Published on 29 Mar 2026 - 8:18

score 380 · Answer 12 · 2026-03-29 07:00:27

380

Views

Am I right to say that "integrally closed extension" and "algebraically closed extension" don't agree in their meaning, even for field extensions?

Published on 29 Mar 2026 - 7:00

score 381 · Answer 13 · 2026-03-22 23:18:21

381

Views

Is : $ \mathrm{Gal} \ : \ F/ \mathbb{Q} \to \mathrm{Gal} (F / \mathbb{Q} ) $ represented by $ \overline{ \mathbb{Q} } $?

Published on 22 Mar 2026 - 23:18

score 852 · Answer 14 · 2026-03-26 06:01:39

852

Views

Show that the field of fractions of $\mathbb{Z}[[x]]$ is properly contained in $\Bbb Q((x))$

Published on 26 Mar 2026 - 6:01

score 143 · Answer 15 · 2026-03-25 04:40:21

143

Views

What does $F^{\times 2}$ mean, for $F$ Field

Published on 25 Mar 2026 - 4:40

List Question

Describe $\mathbb{R}[x]/(x^{2}+ax+b)$ where $a,b \in \mathbb{R}$

Normal closure of a field extension adjoined by a $3$-rd root of unity

Does there exist irreducible polynomials of each degree over arbitrary field?

Proving multiplication is compatible with ordering considering an ordered field.

Proving that $[F(x_1 , x_2) : F] = p_1 p_2$, where $p_1 = \deg \min(x_1 , F)$ and $p_2 = \deg \min(x_2 , F)$ are coprime.

About field of fractions and their classification in the case of $K\left(\eta\right)$

Elementary proof of $\mathcal{O}_K$ is a free abelian group of rank $n$

Is uncountable transcendental-additions enough to make $\mathbb{Q}$ into $\mathbb{R}$?

A simple question about normal closure of field extensions.

Proving that this polynomial has no roots in this field

Is there a field extension that causes polynomials to factor, but not into linear factors?

Am I right to say that "integrally closed extension" and "algebraically closed extension" don't agree in their meaning, even for field extensions?

Is : $ \mathrm{Gal} \ : \ F/ \mathbb{Q} \to \mathrm{Gal} (F / \mathbb{Q} ) $ represented by $ \overline{ \mathbb{Q} } $?

Show that the field of fractions of $\mathbb{Z}[[x]]$ is properly contained in $\Bbb Q((x))$

What does $F^{\times 2}$ mean, for $F$ Field

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