List questions from exact-sequence

Published on 24 Aug 2022 - 23:38

860

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Exact sequences of modules vs. exact sequences of Hom abelian groups

Published on 27 Aug 2022 - 12:00

144

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Bijection between splittings and homomorphisms

Published on 28 Aug 2022 - 15:16

97

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In a 3x3 diagram of modules, if the first two rows are split exact, is the third row also split?

Published on 02 Sep 2022 - 22:01

289

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Exact sequence of modules and freeness

Published on 30 Mar 2026 - 0:34

37

Views

Calculating Ext functor for full abelian subcategory of category of modules over commutative ring

Published on 10 Sep 2022 - 11:23

43

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Find an example of $0\to A\to B\to C\to 0$ and $M$ such that $\mathrm{Hom}_R(B,M)\to\mathrm{Hom}_R(A,M)$ is not surjective

Published on 17 Sep 2022 - 2:49

51

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central extension implies $\frac{G}{Z(G)}\cong \frac{K}{\pi(Z(G))}.$

Published on 17 Sep 2022 - 11:10

168

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For Hirzebruch Surfaces, does the tangent exact sequence split?

Published on 25 Mar 2026 - 11:17

97

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S.E.S.'s in an Abelian Category

Published on 27 Sep 2022 - 16:49

91

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Torsion is "multiplicative"

Published on 07 Oct 2022 - 21:59

41

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A question about the canonical maps $H^i(X,\mathcal{F}) \to H^i(X,sh(\mathcal{F}))$

Published on 09 Oct 2022 - 2:46

210

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Connecting map in the long exact sequence of homotopy groups

Published on 29 Mar 2026 - 11:44

58

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Prove or give counter example: $G \cong N \times G/N \Rightarrow N$ has a normal complement.

Published on 23 Feb 2026 - 20:40

38

Views

Exact sequence $R_K^m→R_K^n→I→0$ given in Silverman's AAEC

Published on 17 Oct 2022 - 6:54

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Question about the term "morphism" in exact and short exact ssequence

Exact sequences of modules vs. exact sequences of Hom abelian groups

Bijection between splittings and homomorphisms

In a 3x3 diagram of modules, if the first two rows are split exact, is the third row also split?

Exact sequence of modules and freeness

Calculating Ext functor for full abelian subcategory of category of modules over commutative ring

Find an example of $0\to A\to B\to C\to 0$ and $M$ such that $\mathrm{Hom}_R(B,M)\to\mathrm{Hom}_R(A,M)$ is not surjective

central extension implies $\frac{G}{Z(G)}\cong \frac{K}{\pi(Z(G))}.$

For Hirzebruch Surfaces, does the tangent exact sequence split?

S.E.S.'s in an Abelian Category

Torsion is "multiplicative"

A question about the canonical maps $H^i(X,\mathcal{F}) \to H^i(X,sh(\mathcal{F}))$

Connecting map in the long exact sequence of homotopy groups

Prove or give counter example: $G \cong N \times G/N \Rightarrow N$ has a normal complement.

Exact sequence $R_K^m→R_K^n→I→0$ given in Silverman's AAEC

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