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Results tagged with homological-algebra
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user 85967
(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.
3
votes
1
answer
2k
views
On an exercise from Weibel's book on homological algebra
I was revising some old postgraduate notes of mine in homological algebra (written during a postgrad course on the topic, I had taken more than ten ;) years ago) and I came accross the following probl …
- 7,746
4
votes
Accepted
Strongly graded algebras with no zero divisors
Yes this is always an isomorphism of $A_0$-bimodules.
It is a general result for strongly graded rings. It holds for an arbitrary grading group $G$ (not necessarily $\mathbb{Z}$) and does not depend …
- 7,746
8
votes
Accepted
$\mathbb{Z}$-graded algebras and tensor products
No it cannot happen.
And not only for strongly $\mathbb{Z}$-graded rings; this is always the case for any strongly $G$-graded ring, where $G$ is a group. $A_k \otimes_{A_0} A_l \simeq A_{k+l}$ is an i …
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1
vote
Dual of a bimodule
I do not know if there is a "standard/correct/natural" method of defining the notion of dual bimodule. A little search i made in the literature did not lead me to smt "standard". In any case, expandin …
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