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(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.
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What is the characteristic of the module over Jacobson semisimple ring?
We know a ring R is semisimple ring iff every module over R is semisimple,a ring R is von-Neumann regular ring iff every module over R is flat,What about the Jacobson semisimple ring?