List questions from exact-sequence

Published on 25 Mar 2026 - 11:00

211

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Short exact sequence splits with $R/I$ quotient ring

Published on 22 Mar 2020 - 21:16

49

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The exact sequence splits iff $gcd(r,s)=1$

Published on 23 Mar 2020 - 3:16

730

Views

Exact sequence of finitely generated abelian groups and alternating sum of ranks equals zero

Published on 25 Mar 2020 - 15:19

411

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Decomposing a group as a direct product of its kernel and image

Published on 26 Mar 2026 - 14:25

1.4k

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Contravariant Hom Functor is Left Exact

Published on 27 Mar 2020 - 0:25

225

Views

Show that if $\mathrm{Hom}(P,-)$ preserves short exact sequences, then $P$ is a projective module

Published on 27 Mar 2020 - 15:31

70

Views

Relation between exact sequences and Hilbert's Nullstellensatz

Published on 27 Mar 2020 - 22:24

99

Views

Understanding proof that $d_n : H_n(S_) \rightarrow H_{n-1}(S_'')$ is a homomorphism for a short exact sequence of complexes.

Published on 31 Mar 2020 - 15:08

208

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Proof about exact sequence

Published on 03 Apr 2020 - 0:12

320

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On subring $R\subseteq S$ such that the inclusion map $i: R\to S$ splits as an $R$-module map

Published on 03 Apr 2020 - 3:34

352

Views

Exact sequence of topological groups induces exact sequence on the fundamental group

Published on 04 Apr 2020 - 1:33

128

Views

I need to prove that exists a homomorphism uniquely determined in a exact sequence

Published on 04 Apr 2020 - 3:22

379

Views

If $M$ and $N$ are divisible, abelian groups, show that their tensor product $M \otimes_\mathbb{Z} N$ is uniquely divisible

Published on 19 Mar 2026 - 19:26

1.1k

Views

Proof of the Nine Lemma using the Snake Lemma

Published on 04 Apr 2020 - 23:47

List Question

Schur-Zassenhaus Theorem

Short exact sequence splits with $R/I$ quotient ring

The exact sequence splits iff $gcd(r,s)=1$

Exact sequence of finitely generated abelian groups and alternating sum of ranks equals zero

Decomposing a group as a direct product of its kernel and image

Contravariant Hom Functor is Left Exact

Show that if $\mathrm{Hom}(P,-)$ preserves short exact sequences, then $P$ is a projective module

Relation between exact sequences and Hilbert's Nullstellensatz

Understanding proof that $d_n : H_n(S_) \rightarrow H_{n-1}(S_'')$ is a homomorphism for a short exact sequence of complexes.

Proof about exact sequence

On subring $R\subseteq S$ such that the inclusion map $i: R\to S$ splits as an $R$-module map

Exact sequence of topological groups induces exact sequence on the fundamental group

I need to prove that exists a homomorphism uniquely determined in a exact sequence

If $M$ and $N$ are divisible, abelian groups, show that their tensor product $M \otimes_\mathbb{Z} N$ is uniquely divisible

Proof of the Nine Lemma using the Snake Lemma

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