Question

Is it possible to describe $Q(x)$ as the extension field of $R$ freely generated by $\{x\}$?

score 217 · Answer 1 · 2026-04-14 15:27:05

217

Views

Is it possible to describe $Q(x)$ as the extension field of $R$ freely generated by $\{x\}$?

Published on 14 Apr 2026 - 15:27

score 48 · Answer 2 · 2026-04-13 02:10:18

48

Views

Equivalence of a integer domain

Published on 13 Apr 2026 - 2:10

score 1.3k · Answer 3 · 2026-05-11 03:49:56

1.3k

Views

Let $F$ be a field and let $R$ be the $F$-subalgebra of $F[x]$ generated by $x^2$ and $x^3.$ Show that $R$ is not a unique factorization domain

Published on 11 May 2026 - 3:49

score 169 · Answer 4 · 2026-04-08 23:58:03

169

Views

Ring structure on $\mathbb{Z}$

Published on 08 Apr 2026 - 23:58

score 139 · Answer 5 · 2026-04-10 15:09:57

139

Views

About units in $\mathbb{Z}[\sqrt[3]{2}]$

Published on 10 Apr 2026 - 15:09

score 392 · Answer 6 · 2026-04-16 05:17:11

392

Views

How to show that $\mathbb{C}[x_1,x_2,x_3, x_4]/(x_1x_2 - x_3x_4, x_1x_3 - x_2x_4, x_1x_4 - x_2x_3)$ is an integral domain?

Published on 16 Apr 2026 - 5:17

score 535 · Answer 7 · 2026-04-13 06:39:48

535

Views

Colon ideal of fractional ideals is itself a fractional ideal

Published on 13 Apr 2026 - 6:39

score 98 · Answer 8 · 2026-04-13 19:05:11

98

Views

In the integral domain $D = \{r+s \sqrt{17}: r,s \in\Bbb Z\}$, which element is irreducible?

Published on 13 Apr 2026 - 19:05

score 427 · Answer 9 · 2026-04-14 01:26:32

427

Views

Unique factorization into irreducible elements?

Published on 14 Apr 2026 - 1:26

score 178 · Answer 10 · 2026-05-11 05:00:08

178

Views

Generalizing the Big Omega function to Integral Domains

Published on 11 May 2026 - 5:00

score 67 · Answer 11 · 2026-04-13 03:58:14

67

Views

Does $ax\in\mathfrak{m}I$ with $x\in I\setminus\mathfrak{m}I$ and $a \in R$ imply $a\in\mathfrak{m}$ for an invertible fractional $R$-ideal $I$?

Published on 13 Apr 2026 - 3:58

score 247 · Answer 12 · 2026-04-11 07:01:16

247

Views

how to define size function in Euclidean domain

Published on 11 Apr 2026 - 7:01

score 2.3k · Answer 13 · 2026-04-15 09:37:51

2.3k

Views

Prove the fractional field of an integral domain is the smallest field containing the integral domain

Published on 15 Apr 2026 - 9:37

score 257 · Answer 14 · 2026-04-13 05:19:31

257

Views

What exactly does it mean for a maximal ideal to be unique in a principal ideal domain?

Published on 13 Apr 2026 - 5:19

score 283 · Answer 15 · 2026-04-11 00:11:20

283

Views

Prove that $S$ is an integral domain and $T$ is not an integral domain.

Published on 11 Apr 2026 - 0:11

List Question

Is it possible to describe $Q(x)$ as the extension field of $R$ freely generated by $\{x\}$?

Equivalence of a integer domain

Let $F$ be a field and let $R$ be the $F$-subalgebra of $F[x]$ generated by $x^2$ and $x^3.$ Show that $R$ is not a unique factorization domain

Ring structure on $\mathbb{Z}$

About units in $\mathbb{Z}[\sqrt[3]{2}]$

How to show that $\mathbb{C}[x_1,x_2,x_3, x_4]/(x_1x_2 - x_3x_4, x_1x_3 - x_2x_4, x_1x_4 - x_2x_3)$ is an integral domain?

Colon ideal of fractional ideals is itself a fractional ideal

In the integral domain $D = \{r+s \sqrt{17}: r,s \in\Bbb Z\}$, which element is irreducible?

Unique factorization into irreducible elements?

Generalizing the Big Omega function to Integral Domains

Does $ax\in\mathfrak{m}I$ with $x\in I\setminus\mathfrak{m}I$ and $a \in R$ imply $a\in\mathfrak{m}$ for an invertible fractional $R$-ideal $I$?

how to define size function in Euclidean domain

Prove the fractional field of an integral domain is the smallest field containing the integral domain

What exactly does it mean for a maximal ideal to be unique in a principal ideal domain?

Prove that $S$ is an integral domain and $T$ is not an integral domain.

Trending Questions

Popular # Hahtags

Popular Questions