Question

prime ideal but not maximal ideal and maximal ideal but not prime ideal

score 2.7k · Answer 1 · 2018-05-07 04:59:52

2.7k

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prime ideal but not maximal ideal and maximal ideal but not prime ideal

Published on 07 May 2018 - 4:59

score 247 · Answer 2 · 2026-03-27 10:31:30

247

Views

Are $\mathbb C[x , y]$ and $ \frac {\mathbb R[x , y]}{ \left<x^2+1 , y\right>}$ PIDs?

Published on 27 Mar 2026 - 10:31

score 194 · Answer 3 · 2018-05-07 14:44:51

194

Views

Ideal generated by $1+2i$ is the same as $(a+bi|a, b \in \mathbb{Z}, 2a=b mod 5)$ in the ring $\mathbb{Z}[i]$ = ($a+bi|a, b \in \mathbb{Z}$

Published on 07 May 2018 - 14:44

score 83 · Answer 4 · 2018-05-07 15:40:58

83

Views

Finding a non-maximal ideal which is comaximal with $(x^2)$ in the polynomial ring.

Published on 07 May 2018 - 15:40

score 298 · Answer 5 · 2018-05-08 20:00:16

298

Views

Construct add/mul tables for the cong classes of the ideal $(x^2+1)$ in the ring $\mathbb{Z}_3[x]$.

Published on 08 May 2018 - 20:00

score 55 · Answer 6 · 2018-05-08 23:21:45

55

Views

Define ideals $I_k$ as $I_k = 2^kR=(2^k a/b | a, b \in \mathbb{Z}, b\text{ odd})$ for ring $R= (a/b|a,b \in \mathbb{Z}, b \space odd)$ and show:

Published on 08 May 2018 - 23:21

score 201 · Answer 7 · 2026-03-25 04:44:16

201

Views

If $f_1,...,f_k$ are given holomorphic functions and $f$ is such that $f_i/f$ is holomorphic then $g_1f_1 + \cdots + g_nf_n = gf$

Published on 25 Mar 2026 - 4:44

score 545 · Answer 8 · 2018-05-10 06:47:36

545

Views

Find a generator of the ideal $I = ⟨x^4 + x^3 − 3x^2 − 5x − 2, x^3 + 3x^2 − 6x − 8⟩ ⊆ \mathbb{Q}[x]$

Published on 10 May 2018 - 6:47

score 196 · Answer 9 · 2018-05-10 18:21:31

196

Views

$\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$

Published on 10 May 2018 - 18:21

score 48 · Answer 10 · 2026-03-25 20:12:44

48

Views

Let $M$ be an irreducible $R$-module and $N$ be the order ideal of $m \in M$. Show that $N$ is maximal in $R_{R}$

Published on 25 Mar 2026 - 20:12

score 218 · Answer 11 · 2026-03-27 10:34:18

218

Views

Kernels of Hopf algebra homomorphisms

Published on 27 Mar 2026 - 10:34

score 391 · Answer 12 · 2018-05-12 14:01:48

391

Views

Finding the ideals of a given norm in a number field

Published on 12 May 2018 - 14:01

score 88 · Answer 13 · 2018-05-13 12:14:56

88

Views

Manipulating ideal generators

Published on 13 May 2018 - 12:14

score 264 · Answer 14 · 2018-05-13 14:18:36

264

Views

Number of generators in an ideal product

Published on 13 May 2018 - 14:18

score 90 · Answer 15 · 2026-03-23 07:06:22

90

Views

Monomial ideal which is not saturated.

Published on 23 Mar 2026 - 7:06

List Question

prime ideal but not maximal ideal and maximal ideal but not prime ideal

Are $\mathbb C[x , y]$ and $ \frac {\mathbb R[x , y]}{ \left<x^2+1 , y\right>}$ PIDs?

Ideal generated by $1+2i$ is the same as $(a+bi|a, b \in \mathbb{Z}, 2a=b mod 5)$ in the ring $\mathbb{Z}[i]$ = ($a+bi|a, b \in \mathbb{Z}$

Finding a non-maximal ideal which is comaximal with $(x^2)$ in the polynomial ring.

Construct add/mul tables for the cong classes of the ideal $(x^2+1)$ in the ring $\mathbb{Z}_3[x]$.

Define ideals $I_k$ as $I_k = 2^kR=(2^k a/b | a, b \in \mathbb{Z}, b\text{ odd})$ for ring $R= (a/b|a,b \in \mathbb{Z}, b \space odd)$ and show:

If $f_1,...,f_k$ are given holomorphic functions and $f$ is such that $f_i/f$ is holomorphic then $g_1f_1 + \cdots + g_nf_n = gf$

Find a generator of the ideal $I = ⟨x^4 + x^3 − 3x^2 − 5x − 2, x^3 + 3x^2 − 6x − 8⟩ ⊆ \mathbb{Q}[x]$

$\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$

Let $M$ be an irreducible $R$-module and $N$ be the order ideal of $m \in M$. Show that $N$ is maximal in $R_{R}$

Kernels of Hopf algebra homomorphisms

Finding the ideals of a given norm in a number field

Manipulating ideal generators

Number of generators in an ideal product

Monomial ideal which is not saturated.

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