Question

Localization of $k[x,y,z]/(xy-z^2)$ at a prime ideal which is different from the maximal graded ideal.

score 226 · Answer 1 · 2021-11-06 10:55:14

226

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Localization of $k[x,y,z]/(xy-z^2)$ at a prime ideal which is different from the maximal graded ideal.

Published on 06 Nov 2021 - 10:55

score 65 · Answer 2 · 2026-03-25 15:59:00

65

Views

Showing that a primary ideal is minimal

Published on 25 Mar 2026 - 15:59

score 132 · Answer 3 · 2026-04-01 04:21:30

132

Views

Localization of $\mathbb{Z}$ at the powers of $15$

Published on 01 Apr 2026 - 4:21

score 75 · Answer 4 · 2026-03-26 21:12:38

75

Views

What are the prime ideals in $\mathbb{Z}[i]$?

Published on 26 Mar 2026 - 21:12

score 86 · Answer 5 · 2021-11-14 16:48:35

86

Views

Prime ideal in $\mathbb{Z}[x,y]$ containing another ideal

Published on 14 Nov 2021 - 16:48

score 43 · Answer 6 · 2026-04-04 16:20:58

43

Views

When and why does $r|m \Rightarrow (p^r - 1)|(p^m-1) \Rightarrow (T^{p^r}-T)|(T^{p^m}- T)$ hold?

Published on 04 Apr 2026 - 16:20

score 76 · Answer 7 · 2021-11-20 12:44:47

76

Views

Exercise about local rings

Published on 20 Nov 2021 - 12:44

score 66 · Answer 8 · 2026-04-05 22:33:39

66

Views

Showing that $A/J \cong \mathbb C.$

Published on 05 Apr 2026 - 22:33

score 463 · Answer 9 · 2021-11-22 16:26:40

463

Views

We say that a ring is "local" when it has only one maximal ideal. Prove that the elements that are out of the maximal ideal are units.

Published on 22 Nov 2021 - 16:26

score 54 · Answer 10 · 2021-11-22 18:58:51

54

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Are $(X+1,X), (X^2+4,5)$ and $(X^2+1,X+2)$ maximal or prime?

Published on 22 Nov 2021 - 18:58

score 33 · Answer 11 · 2026-03-27 06:12:33

33

Views

Find all the ideals $\mathfrak{b}$ that fit $\mathfrak{a}\subsetneq\mathfrak{b}\subsetneq\mathbb{R}[X,Y,Z]$,being$\mathfrak{a}=(X^2-2X-4,Y-X^2,Z-X^3)$

Published on 27 Mar 2026 - 6:12

score 307 · Answer 12 · 2026-03-27 14:56:45

307

Views

Under what conditions will the ring homomorphism $\phi : R \to S$ satisfy the following results about prime and maximal ideals?

Published on 27 Mar 2026 - 14:56

score 340 · Answer 13 · 2021-11-24 15:24:36

340

Views

Show that $(p,\sqrt{d})$ is a prime ideal in $Z[\sqrt{d}]$

Published on 24 Nov 2021 - 15:24

score 415 · Answer 14 · 2021-11-24 15:27:53

415

Views

Prime ideals of $k[t^2,t^3]$

Published on 24 Nov 2021 - 15:27

score 24 · Answer 15 · 2026-03-29 04:02:35

24

Views

Direct proof of two equivalent definitions of a Krull ring

Published on 29 Mar 2026 - 4:02

List Question

Localization of $k[x,y,z]/(xy-z^2)$ at a prime ideal which is different from the maximal graded ideal.

Showing that a primary ideal is minimal

Localization of $\mathbb{Z}$ at the powers of $15$

What are the prime ideals in $\mathbb{Z}[i]$?

Prime ideal in $\mathbb{Z}[x,y]$ containing another ideal

When and why does $r|m \Rightarrow (p^r - 1)|(p^m-1) \Rightarrow (T^{p^r}-T)|(T^{p^m}- T)$ hold?

Exercise about local rings

Showing that $A/J \cong \mathbb C.$

We say that a ring is "local" when it has only one maximal ideal. Prove that the elements that are out of the maximal ideal are units.

Are $(X+1,X), (X^2+4,5)$ and $(X^2+1,X+2)$ maximal or prime?

Find all the ideals $\mathfrak{b}$ that fit $\mathfrak{a}\subsetneq\mathfrak{b}\subsetneq\mathbb{R}[X,Y,Z]$,being$\mathfrak{a}=(X^2-2X-4,Y-X^2,Z-X^3)$

Under what conditions will the ring homomorphism $\phi : R \to S$ satisfy the following results about prime and maximal ideals?

Show that $(p,\sqrt{d})$ is a prime ideal in $Z[\sqrt{d}]$

Prime ideals of $k[t^2,t^3]$

Direct proof of two equivalent definitions of a Krull ring

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