Question

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

score 214 · Answer 1 · 2014-07-16 15:56:42

214

Views

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

Published on 16 Jul 2014 - 15:56

score 45 · Answer 2 · 2014-07-31 05:34:17

45

Views

Equivalence of a integer domain

Published on 31 Jul 2014 - 5:34

score 1.3k · Answer 3 · 2014-08-02 08:00:36

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 02 Aug 2014 - 8:00

score 166 · Answer 4 · 2014-08-06 09:40:23

166

Views

Ring structure on $\mathbb{Z}$

Published on 06 Aug 2014 - 9:40

score 136 · Answer 5 · 2014-08-12 20:12:41

136

Views

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

Published on 12 Aug 2014 - 20:12

score 389 · Answer 6 · 2014-09-20 16:03:27

389

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 20 Sep 2014 - 16:03

score 532 · Answer 7 · 2014-09-21 03:04:30

532

Views

Colon ideal of fractional ideals is itself a fractional ideal

Published on 21 Sep 2014 - 3:04

score 95 · Answer 8 · 2014-09-23 20:56:30

95

Views

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

Published on 23 Sep 2014 - 20:56

score 424 · Answer 9 · 2014-09-27 21:25:21

424

Views

Unique factorization into irreducible elements?

Published on 27 Sep 2014 - 21:25

score 174 · Answer 10 · 2014-10-04 00:18:17

174

Views

Generalizing the Big Omega function to Integral Domains

Published on 04 Oct 2014 - 0:18

score 64 · Answer 11 · 2014-10-05 14:48:13

64

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 05 Oct 2014 - 14:48

score 244 · Answer 12 · 2014-10-07 17:21:49

244

Views

how to define size function in Euclidean domain

Published on 07 Oct 2014 - 17:21

score 2.3k · Answer 13 · 2014-10-11 18:50:09

2.3k

Views

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

Published on 11 Oct 2014 - 18:50

score 254 · Answer 14 · 2014-10-14 18:06:23

254

Views

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

Published on 14 Oct 2014 - 18:06

score 280 · Answer 15 · 2014-10-20 00:16:20

280

Views

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

Published on 20 Oct 2014 - 0:16

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.

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