Question

If $\mathrm{Ext}^n_R (M,R/\mathrm{rad}(R))=0$ for all $n\geq 1$, then $\mathrm{Ext}^n_R (M,N)=0$ for all $n\geq 1$.

score 110 · Answer 1 · 2026-03-29 14:59:08

110

Views

If $\mathrm{Ext}^n_R (M,R/\mathrm{rad}(R))=0$ for all $n\geq 1$, then $\mathrm{Ext}^n_R (M,N)=0$ for all $n\geq 1$.

Published on 29 Mar 2026 - 14:59

score 38 · Answer 2 · 2026-03-25 17:52:08

38

Views

$\cdots \to H^{p+n} \rightarrow E_{2}^{p, n} \to E_{2}^{p+n+1,0} \to H^{p+n+1} \to E_{2}^{p+1, n} \to E_{2}^{p+n+2,0} \to \cdots$

Published on 25 Mar 2026 - 17:52

score 198 · Answer 3 · 2020-04-28 19:57:36

198

Views

Explicit isomorphism $H^n(X;\Bbb Z)\otimes \Bbb Z_p\to H^n(X;\Bbb Z_p)$ when $H_i(X)$ are finitely generated free abelian for all $i$.

Published on 28 Apr 2020 - 19:57

score 253 · Answer 4 · 2026-03-31 08:11:47

253

Views

The derived category of the dual numbers?

Published on 31 Mar 2026 - 8:11

score 406 · Answer 5 · 2026-03-26 14:30:25

406

Views

Injective resolution of $K$ as a $K[x]/x^n$-module

Published on 26 Mar 2026 - 14:30

score 581 · Answer 6 · 2026-03-25 17:53:05

581

Views

Has anyone seen this generalization of the snake lemma? Is it useful?

Published on 25 Mar 2026 - 17:53

score 130 · Answer 7 · 2026-03-25 03:00:52

130

Views

Why doesn't the Homotopy group satisfy excision?

Published on 25 Mar 2026 - 3:00

score 45 · Answer 8 · 2020-04-30 13:46:36

45

Views

Collection of maps on a split abelian complex

Published on 30 Apr 2020 - 13:46

score 121 · Answer 9 · 2026-03-26 04:50:43

121

Views

Colimits in triangulated categories

Published on 26 Mar 2026 - 4:50

score 279 · Answer 10 · 2020-04-30 17:27:55

279

Views

Let $D$ be an integral domain which is not field and $Q=\text{Frac}(D)$. Then $Q$ has not a projective cover as $D$-module.

Published on 30 Apr 2020 - 17:27

score 178 · Answer 11 · 2026-03-27 10:10:11

178

Views

Explicit description of all extensions of $\mathbf{Z}/n\mathbf{Z}$ by $\mathbf{Z}$

Published on 27 Mar 2026 - 10:10

score 96 · Answer 12 · 2026-03-28 02:48:25

96

Views

When does a finitely generated projective module surjects onto the ring

Published on 28 Mar 2026 - 2:48

score 180 · Answer 13 · 2020-05-01 16:12:43

180

Views

Yoneda product in the cohomology of a truncated polynomial algebra

Published on 01 May 2020 - 16:12

score 341 · Answer 14 · 2020-05-01 16:15:50

341

Views

Duality between homology and cohomology of complexes and the Kroenecker morphism

Published on 01 May 2020 - 16:15

score 90 · Answer 15 · 2020-05-01 18:05:41

90

Views

Finding the singular homology of the quotient of the disjoint union of two spaces

Published on 01 May 2020 - 18:05

List Question

If $\mathrm{Ext}^n_R (M,R/\mathrm{rad}(R))=0$ for all $n\geq 1$, then $\mathrm{Ext}^n_R (M,N)=0$ for all $n\geq 1$.

$\cdots \to H^{p+n} \rightarrow E_{2}^{p, n} \to E_{2}^{p+n+1,0} \to H^{p+n+1} \to E_{2}^{p+1, n} \to E_{2}^{p+n+2,0} \to \cdots$

Explicit isomorphism $H^n(X;\Bbb Z)\otimes \Bbb Z_p\to H^n(X;\Bbb Z_p)$ when $H_i(X)$ are finitely generated free abelian for all $i$.

The derived category of the dual numbers?

Injective resolution of $K$ as a $K[x]/x^n$-module

Has anyone seen this generalization of the snake lemma? Is it useful?

Why doesn't the Homotopy group satisfy excision?

Collection of maps on a split abelian complex

Colimits in triangulated categories

Let $D$ be an integral domain which is not field and $Q=\text{Frac}(D)$. Then $Q$ has not a projective cover as $D$-module.

Explicit description of all extensions of $\mathbf{Z}/n\mathbf{Z}$ by $\mathbf{Z}$

When does a finitely generated projective module surjects onto the ring

Yoneda product in the cohomology of a truncated polynomial algebra

Duality between homology and cohomology of complexes and the Kroenecker morphism

Finding the singular homology of the quotient of the disjoint union of two spaces

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