Question

The ideal $(X,Y)$ is prime in $\mathbb{C}[X,Y]$. But is it also maximal?

score 256 · Answer 1 · 2012-10-23 21:09:27

256

Views

The ideal $(X,Y)$ is prime in $\mathbb{C}[X,Y]$. But is it also maximal?

Published on 23 Oct 2012 - 21:09

score 12.3k · Answer 2 · 2026-03-25 14:18:33

12.3k

Views

Division algorithm for multivariate polynomials?

Published on 25 Mar 2026 - 14:18

score 393 · Answer 3 · 2020-08-20 11:54:15

393

Views

Is $f(\sqrt 2)$ in $\Bbb Q[\sqrt 2]$ where $f\in\Bbb Q[x]$?

Published on 20 Aug 2020 - 11:54

score 32 · Answer 4 · 2020-08-23 13:14:02

32

Views

Description of the elements of (p(x))\(q(x))

Published on 23 Aug 2020 - 13:14

score 172 · Answer 5 · 2020-08-24 17:31:50

172

Views

Factor $x^8 + x^2 + 13$ into irreducible polynomials in $\Bbb F_{23} [x]$.

Published on 24 Aug 2020 - 17:31

score 872 · Answer 6 · 2020-08-24 18:45:23

872

Views

Show that $x^7 + x^6 + x^5 + x^4 + x^2 + x + 1$ is a primitive polynomial over $Z_2$.

Published on 24 Aug 2020 - 18:45

score 149 · Answer 7 · 2020-08-24 21:32:14

149

Views

If $I$ and $J$ are ideals and I know an algorithm to find $I : J$, can I use this to find the saturation of $I$ by $J$?

Published on 24 Aug 2020 - 21:32

score 49 · Answer 8 · 2020-09-11 06:31:50

49

Views

Prove that $P[x] + \langle x \rangle$ is a prime ideal of $R[x].$

Published on 11 Sep 2020 - 6:31

score 67 · Answer 9 · 2020-09-12 12:23:26

67

Views

Is $x^n - y^m$ irreducible ($n, m$ strictly positive integers with $n \ne m$)?

Published on 12 Sep 2020 - 12:23

score 35 · Answer 10 · 2020-09-16 19:05:21

35

Views

Let $ R = \mathbb{Z}_8$. Find a nonzero polynomial $f$ in $R[x]$ of degree at most 3 such that each element of $R$ is a root of $f$.

Published on 16 Sep 2020 - 19:05

score 282 · Answer 11 · 2020-09-18 16:03:27

282

Views

Let $I=\langle 4, 2x,x^{2} \rangle$ in $\mathbb{Z[x]}$. Show that $I$ can not be generated by 2 elements.

Published on 18 Sep 2020 - 16:03

score 45 · Answer 12 · 2020-09-19 06:34:23

45

Views

Showing a sum in a field of fractions is nonzero

Published on 19 Sep 2020 - 6:34

score 446 · Answer 13 · 2020-10-13 08:59:03

446

Views

The spectrum of $\mathbb{Q}[x,y]/(x^2,xy)$

Published on 13 Oct 2020 - 8:59

score 1k · Answer 14 · 2020-10-13 11:14:08

1k

Views

What is the characteristic of the polynomial ring $\mathbb{Z}_6[x]$?

Published on 13 Oct 2020 - 11:14

score 539 · Answer 15 · 2020-10-29 12:19:15

539

Views

How can a polynomial ring be finitely generated?

Published on 29 Oct 2020 - 12:19

List Question

The ideal $(X,Y)$ is prime in $\mathbb{C}[X,Y]$. But is it also maximal?

Division algorithm for multivariate polynomials?

Is $f(\sqrt 2)$ in $\Bbb Q[\sqrt 2]$ where $f\in\Bbb Q[x]$?

Description of the elements of (p(x))\(q(x))

Factor $x^8 + x^2 + 13$ into irreducible polynomials in $\Bbb F_{23} [x]$.

Show that $x^7 + x^6 + x^5 + x^4 + x^2 + x + 1$ is a primitive polynomial over $Z_2$.

If $I$ and $J$ are ideals and I know an algorithm to find $I : J$, can I use this to find the saturation of $I$ by $J$?

Prove that $P[x] + \langle x \rangle$ is a prime ideal of $R[x].$

Is $x^n - y^m$ irreducible ($n, m$ strictly positive integers with $n \ne m$)?

Let $ R = \mathbb{Z}_8$. Find a nonzero polynomial $f$ in $R[x]$ of degree at most 3 such that each element of $R$ is a root of $f$.

Let $I=\langle 4, 2x,x^{2} \rangle$ in $\mathbb{Z[x]}$. Show that $I$ can not be generated by 2 elements.

Showing a sum in a field of fractions is nonzero

The spectrum of $\mathbb{Q}[x,y]/(x^2,xy)$

What is the characteristic of the polynomial ring $\mathbb{Z}_6[x]$?

How can a polynomial ring be finitely generated?

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