List questions from homological-algebra

Published on 29 Dec 2016 - 21:03

79

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Need help understanding the proof that every free module is projective.

Published on 30 Dec 2016 - 10:03

223

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A question about short exact sequences

Published on 28 Mar 2026 - 2:42

1.3k

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Prove that $\mathrm{Tor}_1^R(R/I,R/J)=(I\cap J)/(IJ)$

Published on 01 Jan 2017 - 17:59

305

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Why does $\mathrm{Tor}_0^R(M,N)\cong M\otimes_R N$?

Published on 01 Jan 2017 - 18:55

88

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Showing that filtered complexes induce a spectral sequence

Published on 25 Mar 2026 - 22:30

146

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Two questions about torsionless modules

Published on 03 Jan 2017 - 9:42

233

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Dualizing the statement "left exact iff preserves kernels"

Published on 28 Mar 2026 - 0:47

31

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$pd_{\Lambda /I} B < \infty$ induces $pd_{\Lambda} B < \infty$

Published on 04 Jan 2017 - 13:21

251

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Show that $H^G(X\times Y)\cong H^G(X)\times H^G(Y)$

Published on 28 Mar 2026 - 8:50

199

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How do I prove $\operatorname{Hom}_R(A, B)$ torsion-free and divisible under the given conditions, where $A$ and $B$ are abelian groups.

Published on 04 Jan 2017 - 16:44

130

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Categorical construction - do I have a functor?

Published on 26 Mar 2026 - 6:20

101

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How to get the projective dimension just by a non-split sequence?

Published on 05 Jan 2017 - 2:45

82

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Euler-Poincaré characteristic of an acyclic chain complex (from Lang's Algebra)

Published on 05 Jan 2017 - 12:07

88

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Isomorphisms between dual vector spaces

Published on 25 Mar 2026 - 22:01

List Question

Extensions are classified by $Ext^1(C, A)$: should one apply $Hom(\cdot, A)$ or $Hom(C, \cdot)$?

Need help understanding the proof that every free module is projective.

A question about short exact sequences

Prove that $\mathrm{Tor}_1^R(R/I,R/J)=(I\cap J)/(IJ)$

Why does $\mathrm{Tor}_0^R(M,N)\cong M\otimes_R N$?

Showing that filtered complexes induce a spectral sequence

Two questions about torsionless modules

Dualizing the statement "left exact iff preserves kernels"

$pd_{\Lambda /I} B < \infty$ induces $pd_{\Lambda} B < \infty$

Show that $H^G(X\times Y)\cong H^G(X)\times H^G(Y)$

How do I prove $\operatorname{Hom}_R(A, B)$ torsion-free and divisible under the given conditions, where $A$ and $B$ are abelian groups.

Categorical construction - do I have a functor?

How to get the projective dimension just by a non-split sequence?

Euler-Poincaré characteristic of an acyclic chain complex (from Lang's Algebra)

Isomorphisms between dual vector spaces

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