Question

Why $\mathfrak{p}A_\mathfrak{p} = 0$, where $A_{\mathfrak p}$ is the localization at the kernel $\mathfrak p$ of a surjective ring homomorphism.

score 73 · Answer 1 · 2026-03-29 15:03:43

73

Views

Why $\mathfrak{p}A_\mathfrak{p} = 0$, where $A_{\mathfrak p}$ is the localization at the kernel $\mathfrak p$ of a surjective ring homomorphism.

Published on 29 Mar 2026 - 15:03

score 174 · Answer 2 · 2022-04-17 21:50:48

174

Views

If $A$ is Noetherian, and $x$ is a non-unit and non zero-divisor, then can $(xr)=(r)$ for any non-unit $r$?

Published on 17 Apr 2022 - 21:50

score 60 · Answer 3 · 2022-04-20 07:31:54

60

Views

Can generators of Noether normalization be zero divisors?

Published on 20 Apr 2022 - 7:31

score 100 · Answer 4 · 2026-03-29 22:44:54

100

Views

$M/xM$ free over $R/xR$ implies $M$ is free over $R$ when $R$ Noetherian

Published on 29 Mar 2026 - 22:44

score 52 · Answer 5 · 2022-05-04 12:04:25

52

Views

A question related to the dimension of a ring

Published on 04 May 2022 - 12:04

score 35 · Answer 6 · 2022-05-05 11:23:21

35

Views

Lifting Property of flips

Published on 05 May 2022 - 11:23

score 42 · Answer 7 · 2026-03-29 21:58:23

42

Views

Relation between height of an ideal and unimodular row

Published on 29 Mar 2026 - 21:58

score 109 · Answer 8 · 2022-05-09 06:45:47

109

Views

Unimodular element of a module

Published on 09 May 2022 - 6:45

score 43 · Answer 9 · 2026-03-28 00:48:09

43

Views

When $\mathrm{Hom}$ functor commutes with colimits in a category of modules?

Published on 28 Mar 2026 - 0:48

score 114 · Answer 10 · 2026-03-26 02:55:47

114

Views

Showing that $R/\operatorname{ann}(A)$ is artinian

Published on 26 Mar 2026 - 2:55

score 68 · Answer 11 · 2022-05-18 11:01:21

68

Views

If $A$ is a ring, why isn’t the ideal $A^{(\mathbb{N})}\subset A^\mathbb{N}$ finitely generated?

Published on 18 May 2022 - 11:01

score 283 · Answer 12 · 2022-05-20 05:47:12

283

Views

Is $\bigcap_{n=1}^\infty I^n$ contained in a minimal prime ideal?

Published on 20 May 2022 - 5:47

score 169 · Answer 13 · 2026-03-26 00:53:43

169

Views

A is noetherian and every prime ideal of A is maximal then...

Published on 26 Mar 2026 - 0:53

score 126 · Answer 14 · 2022-05-22 18:41:53

126

Views

Find the radical of an ideal in the ring of polynomials over the complex numbers

Published on 22 May 2022 - 18:41

score 30 · Answer 15 · 2026-03-26 02:34:53

30

Views

Examples?? Surjective (resp. Injective) ring endomorphisms which aren't isomorphisms

Published on 26 Mar 2026 - 2:34

List Question

Why $\mathfrak{p}A_\mathfrak{p} = 0$, where $A_{\mathfrak p}$ is the localization at the kernel $\mathfrak p$ of a surjective ring homomorphism.

If $A$ is Noetherian, and $x$ is a non-unit and non zero-divisor, then can $(xr)=(r)$ for any non-unit $r$?

Can generators of Noether normalization be zero divisors?

$M/xM$ free over $R/xR$ implies $M$ is free over $R$ when $R$ Noetherian

A question related to the dimension of a ring

Lifting Property of flips

Relation between height of an ideal and unimodular row

Unimodular element of a module

When $\mathrm{Hom}$ functor commutes with colimits in a category of modules?

Showing that $R/\operatorname{ann}(A)$ is artinian

If $A$ is a ring, why isn’t the ideal $A^{(\mathbb{N})}\subset A^\mathbb{N}$ finitely generated?

Is $\bigcap_{n=1}^\infty I^n$ contained in a minimal prime ideal?

A is noetherian and every prime ideal of A is maximal then...

Find the radical of an ideal in the ring of polynomials over the complex numbers

Examples?? Surjective (resp. Injective) ring endomorphisms which aren't isomorphisms

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