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Results tagged with homological-algebra
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user 4213
(Co)chain complexes, abelian Categories, (pre)sheaves, (co)homology in various (possibly highly generalized) settings, spectra, derived functors, resolutions, spectral sequences, homotopy categories. Chain complexes in an abelian category form the heart of homological algebra.
7
votes
5
votes
Accepted
Notation for algebras
It's pretty standard to use $\bigwedge(V)$ or $\Lambda(V)$ for the exterior
algebra on a vector space $V$ and $\bigwedge^k(V)$ or $\Lambda^k(V)$
for the $k$-th graded part. For symmetric algebras $S(V …
- 20.8k
8
votes
Accepted
Projective dimension
No. A submodule of a free module need not have finite projective dimension.
As a simple example let $R=\mathbb{Z}/p^2\mathbb{Z}$. The free module $R$
has a submodule $p\mathbb{Z}/p^2\mathbb{Z}\cong\ma …
- 20.8k