Question

Prove that for a commutative Noetherian ring $A$ with $\mathrm{Spec}(A)$ finite and discrete, $\ker(f_r)=\{0\}$ implies $f_r$ is surjective.

score 205 · Answer 1 · 2026-03-25 20:14:13

205

Views

Prove that for a commutative Noetherian ring $A$ with $\mathrm{Spec}(A)$ finite and discrete, $\ker(f_r)=\{0\}$ implies $f_r$ is surjective.

Published on 25 Mar 2026 - 20:14

score 247 · Answer 2 · 2026-03-25 20:09:42

247

Views

Short exact sequence of modules over Artinian local ring

Published on 25 Mar 2026 - 20:09

score 47 · Answer 3 · 2026-03-25 20:08:03

47

Views

$\Lambda/\mathfrak{r}\cong \operatorname{soc}(\Lambda)$ as a criterion for self-injectivity

Published on 25 Mar 2026 - 20:08

score 170 · Answer 4 · 2026-03-25 20:13:57

170

Views

Is an artinian subring of a local artinian ring local?

Published on 25 Mar 2026 - 20:13

score 104 · Answer 5 · 2026-05-10 17:06:16

104

Views

Colon property in artinian local Gorenstein

Published on 10 May 2026 - 17:06

score 44 · Answer 6 · 2026-03-25 20:09:46

44

Views

for an endomorphism $f$ over an Artinian module

Published on 25 Mar 2026 - 20:09

score 237 · Answer 7 · 2026-03-25 20:14:17

237

Views

How to show $\operatorname{ann}(M) = \operatorname{ann}(X)$.

Published on 25 Mar 2026 - 20:14

score 103 · Answer 8 · 2026-03-25 20:08:39

103

Views

Commutative local Artinian ring without a section in characteristic $0$

Published on 25 Mar 2026 - 20:08

score 59 · Answer 9 · 2026-03-25 20:11:15

59

Views

Understanding the Proof of Maschkes's Theorem

Published on 25 Mar 2026 - 20:11

score 112 · Answer 10 · 2026-03-25 20:13:53

112

Views

The ring $\Bbb Q[x,y,z]/(x^a,y^b,z^c)$ is noetherian

Published on 25 Mar 2026 - 20:13

score 160 · Answer 11 · 2026-03-25 20:08:31

160

Views

Does a finitely generated faithful module over an Artinian ring contain a regular element?

Published on 25 Mar 2026 - 20:08

score 124 · Answer 12 · 2026-03-25 20:13:49

124

Views

An Exercise on projective covers and injective envelopes of simple modules over an Artin algebra

Published on 25 Mar 2026 - 20:13

score 113 · Answer 13 · 2026-03-25 20:07:33

113

Views

Question on injective envelopes

Published on 25 Mar 2026 - 20:07

score 240 · Answer 14 · 2026-03-25 20:14:17

240

Views

Prove that the ring is Artinian and find a composition series of ideals

Published on 25 Mar 2026 - 20:14

score 49 · Answer 15 · 2026-03-25 20:11:19

49

Views

Find composition series of Αrtinian ring, that is finite dimensional vector space

Published on 25 Mar 2026 - 20:11

List Question

Prove that for a commutative Noetherian ring $A$ with $\mathrm{Spec}(A)$ finite and discrete, $\ker(f_r)=\{0\}$ implies $f_r$ is surjective.

Short exact sequence of modules over Artinian local ring

$\Lambda/\mathfrak{r}\cong \operatorname{soc}(\Lambda)$ as a criterion for self-injectivity

Is an artinian subring of a local artinian ring local?

Colon property in artinian local Gorenstein

for an endomorphism $f$ over an Artinian module

How to show $\operatorname{ann}(M) = \operatorname{ann}(X)$.

Commutative local Artinian ring without a section in characteristic $0$

Understanding the Proof of Maschkes's Theorem

The ring $\Bbb Q[x,y,z]/(x^a,y^b,z^c)$ is noetherian

Does a finitely generated faithful module over an Artinian ring contain a regular element?

An Exercise on projective covers and injective envelopes of simple modules over an Artin algebra

Question on injective envelopes

Prove that the ring is Artinian and find a composition series of ideals

Find composition series of Αrtinian ring, that is finite dimensional vector space

Trending Questions

Popular # Hahtags

Popular Questions