Question

If $M$ is a finitely generated module over a Noetherian ring $A,$ then $\widehat{\mathfrak{a}M}=\hat{\mathfrak{a}} \hat{M}$

score 246 · Answer 1 · 2026-04-01 16:48:22

246

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If $M$ is a finitely generated module over a Noetherian ring $A,$ then $\widehat{\mathfrak{a}M}=\hat{\mathfrak{a}} \hat{M}$

Published on 01 Apr 2026 - 16:48

score 318 · Answer 2 · 2026-03-29 01:35:42

318

Views

Map between stalks induced by a finite morphism is finite

Published on 29 Mar 2026 - 1:35

score 76 · Answer 3 · 2026-04-04 01:51:50

76

Views

The number of polynomial functions $f:A\to A$ is $|A|^2$ if and only if $x^2=x$ for all $x\in A$.

Published on 04 Apr 2026 - 1:51

score 104 · Answer 4 · 2026-03-25 06:06:23

104

Views

On derived functors of certain $\operatorname{Tor}_1$ and $\operatorname{Ext}^1$

Published on 25 Mar 2026 - 6:06

score 135 · Answer 5 · 2026-03-25 09:28:31

135

Views

The finite generation of $M$, to conclude $M$ is Noetherian (when $R$ is Noetherian).

Published on 25 Mar 2026 - 9:28

score 275 · Answer 6 · 2026-03-25 07:41:43

275

Views

Prove that the quotient ring is not a PID

Published on 25 Mar 2026 - 7:41

score 167 · Answer 7 · 2026-03-29 08:20:56

167

Views

Irreducibility of generators of maximal ideal

Published on 29 Mar 2026 - 8:20

score 207 · Answer 8 · 2026-03-26 18:50:30

207

Views

Is $x$ always irreducible in the quotient ring

Published on 26 Mar 2026 - 18:50

score 496 · Answer 9 · 2026-02-23 04:19:04

496

Views

$K[X]_X$ is not integral over $K[X]$

Published on 23 Feb 2026 - 4:19

score 669 · Answer 10 · 2026-03-25 09:39:57

669

Views

Proving $y-x^2, z-xy$ generate the ideal of the twisted cubic

Published on 25 Mar 2026 - 9:39

score 269 · Answer 11 · 2026-04-04 09:54:08

269

Views

How to show that $2$ is invertible in a ring with odd cardinality?

Published on 04 Apr 2026 - 9:54

score 530 · Answer 12 · 2026-03-24 20:36:52

530

Views

A question about Integral Closures from Hartshorne Chapter 2 Exercise 6.4

Published on 24 Mar 2026 - 20:36

score 990 · Answer 13 · 2026-03-26 08:00:35

990

Views

Show that every non-zero ideal of the ring of rationals with odd denominator is generated by $2^{n}$

Published on 26 Mar 2026 - 8:00

score 52 · Answer 14 · 2026-03-25 07:15:36

52

Views

A homomorphism on a nontrivial commutative ring with trivial unit group

Published on 25 Mar 2026 - 7:15

score 496 · Answer 15 · 2026-03-25 10:57:17

496

Views

Subring of polynomial ring containing two polynomials of relatively prime degree

Published on 25 Mar 2026 - 10:57

List Question

If $M$ is a finitely generated module over a Noetherian ring $A,$ then $\widehat{\mathfrak{a}M}=\hat{\mathfrak{a}} \hat{M}$

Map between stalks induced by a finite morphism is finite

The number of polynomial functions $f:A\to A$ is $|A|^2$ if and only if $x^2=x$ for all $x\in A$.

On derived functors of certain $\operatorname{Tor}_1$ and $\operatorname{Ext}^1$

The finite generation of $M$, to conclude $M$ is Noetherian (when $R$ is Noetherian).

Prove that the quotient ring is not a PID

Irreducibility of generators of maximal ideal

Is $x$ always irreducible in the quotient ring

$K[X]_X$ is not integral over $K[X]$

Proving $y-x^2, z-xy$ generate the ideal of the twisted cubic

How to show that $2$ is invertible in a ring with odd cardinality?

A question about Integral Closures from Hartshorne Chapter 2 Exercise 6.4

Show that every non-zero ideal of the ring of rationals with odd denominator is generated by $2^{n}$

A homomorphism on a nontrivial commutative ring with trivial unit group

Subring of polynomial ring containing two polynomials of relatively prime degree

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