Question

Show that $\operatorname{spec}(K[x_1,\dots,x_n])=\cup_{L/K}\operatorname{Im}(\psi_L)$ where $\psi_F(a)=\ker(f\mapsto f(a))$

score 36 · Answer 1 · 2019-08-25 13:03:09

36

Views

Show that $\operatorname{spec}(K[x_1,\dots,x_n])=\cup_{L/K}\operatorname{Im}(\psi_L)$ where $\psi_F(a)=\ker(f\mapsto f(a))$

Published on 25 Aug 2019 - 13:03

score 418 · Answer 2 · 2026-03-27 10:48:01

418

Views

Number of maximal ideals of a subring of $\mathbb{Q}$

Published on 27 Mar 2026 - 10:48

score 307 · Answer 3 · 2019-08-27 11:30:51

307

Views

If (ideals) $J\subseteq I_1\cup\dots\cup I_n$ and $I_3,\dots,I_n$ are prime then $J\subseteq I_k$

Published on 27 Aug 2019 - 11:30

score 195 · Answer 4 · 2026-03-27 10:53:00

195

Views

Norm of an element at a localization

Published on 27 Mar 2026 - 10:53

score 164 · Answer 5 · 2019-08-30 17:00:50

164

Views

If $R/(x)$ is finite, every non-zero prime ideal of $R$ is maximal

Published on 30 Aug 2019 - 17:00

score 740 · Answer 6 · 2026-03-25 07:42:44

740

Views

Integral ring homomorphism implies induced map on spectra is closed

Published on 25 Mar 2026 - 7:42

score 73 · Answer 7 · 2019-09-13 20:49:09

73

Views

$I$ is prime ideal in $k[x_1, \dots , x_n]$ iif $I^h$ is prime ideal in $k[x_0, \dots , x_n]$

Published on 13 Sep 2019 - 20:49

score 51 · Answer 8 · 2026-03-27 10:47:51

51

Views

Prove that $\psi:\text{spec}(R_p)\to\text{spec} R$ is injective and $\text{Im}\psi=\{q\in\text{spec} R:q\subseteq p\}$

Published on 27 Mar 2026 - 10:47

score 342 · Answer 9 · 2019-09-20 14:04:42

342

Views

If $M$ is a finitely generated module then $\sqrt{\text{ann}(M)}=\bigcap\text{supp}(M)$

Published on 20 Sep 2019 - 14:04

score 121 · Answer 10 · 2026-03-27 12:30:15

121

Views

If $I$ is an ideal and $M$ is a (finitely generated) module then $\text{Supp}(M/IM)\subseteq_{(=)}\text{Supp}(M)\cap V(I)$

Published on 27 Mar 2026 - 12:30

score 79 · Answer 11 · 2019-09-20 20:50:48

79

Views

Find $\mathbb Z$-modules $L,K\subseteq M:=\mathbb Z\oplus(\mathbb Z/2019\mathbb Z)$ s.t. $L+K=M$ & $\text{Ass}(L)\cup\text{Ass}(K)\ne\text{Ass}(M)$

Published on 20 Sep 2019 - 20:50

score 133 · Answer 12 · 2026-03-27 12:27:29

133

Views

If $M_p$ is a localization, why doesn't $M_p=0$ imply $M=0$?

Published on 27 Mar 2026 - 12:27

score 411 · Answer 13 · 2019-09-22 01:09:48

411

Views

Maximal ideal of $\mathbb{C}[x]/(x^2+1)$

Published on 22 Sep 2019 - 1:09

score 101 · Answer 14 · 2019-09-22 17:56:14

101

Views

Find an example of a commutatice unital ring $R$ and an $R$-module such that $\text{Ass}(M)=\emptyset$

Published on 22 Sep 2019 - 17:56

score 146 · Answer 15 · 2026-03-25 05:02:14

146

Views

Primacy of ideals in a cyclotomic field

Published on 25 Mar 2026 - 5:02

List Question

Show that $\operatorname{spec}(K[x_1,\dots,x_n])=\cup_{L/K}\operatorname{Im}(\psi_L)$ where $\psi_F(a)=\ker(f\mapsto f(a))$

Number of maximal ideals of a subring of $\mathbb{Q}$

If (ideals) $J\subseteq I_1\cup\dots\cup I_n$ and $I_3,\dots,I_n$ are prime then $J\subseteq I_k$

Norm of an element at a localization

If $R/(x)$ is finite, every non-zero prime ideal of $R$ is maximal

Integral ring homomorphism implies induced map on spectra is closed

$I$ is prime ideal in $k[x_1, \dots , x_n]$ iif $I^h$ is prime ideal in $k[x_0, \dots , x_n]$

Prove that $\psi:\text{spec}(R_p)\to\text{spec} R$ is injective and $\text{Im}\psi=\{q\in\text{spec} R:q\subseteq p\}$

If $M$ is a finitely generated module then $\sqrt{\text{ann}(M)}=\bigcap\text{supp}(M)$

If $I$ is an ideal and $M$ is a (finitely generated) module then $\text{Supp}(M/IM)\subseteq_{(=)}\text{Supp}(M)\cap V(I)$

Find $\mathbb Z$-modules $L,K\subseteq M:=\mathbb Z\oplus(\mathbb Z/2019\mathbb Z)$ s.t. $L+K=M$ & $\text{Ass}(L)\cup\text{Ass}(K)\ne\text{Ass}(M)$

If $M_p$ is a localization, why doesn't $M_p=0$ imply $M=0$?

Maximal ideal of $\mathbb{C}[x]/(x^2+1)$

Find an example of a commutatice unital ring $R$ and an $R$-module such that $\text{Ass}(M)=\emptyset$

Primacy of ideals in a cyclotomic field

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