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 204 · Answer 1 · 2020-08-14 15:53:29

204

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 14 Aug 2020 - 15:53

score 246 · Answer 2 · 2020-08-23 01:30:57

246

Views

Short exact sequence of modules over Artinian local ring

Published on 23 Aug 2020 - 1:30

score 46 · Answer 3 · 2020-09-09 23:06:54

46

Views

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

Published on 09 Sep 2020 - 23:06

score 169 · Answer 4 · 2020-09-18 17:34:50

169

Views

Is an artinian subring of a local artinian ring local?

Published on 18 Sep 2020 - 17:34

score 100 · Answer 5 · 2026-03-25 09:16:19

100

Views

Colon property in artinian local Gorenstein

Published on 25 Mar 2026 - 9:16

score 43 · Answer 6 · 2020-10-07 14:14:46

43

Views

for an endomorphism $f$ over an Artinian module

Published on 07 Oct 2020 - 14:14

score 236 · Answer 7 · 2020-10-19 21:25:18

236

Views

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

Published on 19 Oct 2020 - 21:25

score 102 · Answer 8 · 2020-11-11 01:57:29

102

Views

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

Published on 11 Nov 2020 - 1:57

score 58 · Answer 9 · 2020-11-26 21:05:02

58

Views

Understanding the Proof of Maschkes's Theorem

Published on 26 Nov 2020 - 21:05

score 111 · Answer 10 · 2020-12-16 05:25:15

111

Views

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

Published on 16 Dec 2020 - 5:25

score 159 · Answer 11 · 2020-12-25 22:04:06

159

Views

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

Published on 25 Dec 2020 - 22:04

score 123 · Answer 12 · 2021-01-06 12:17:00

123

Views

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

Published on 06 Jan 2021 - 12:17

score 112 · Answer 13 · 2021-01-06 12:44:16

112

Views

Question on injective envelopes

Published on 06 Jan 2021 - 12:44

score 239 · Answer 14 · 2021-01-06 17:27:35

239

Views

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

Published on 06 Jan 2021 - 17:27

score 48 · Answer 15 · 2021-01-07 01:22:52

48

Views

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

Published on 07 Jan 2021 - 1:22

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

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