An introduction to homological algebra. (English) Zbl 0441.18018


18Gxx Homological algebra in category theory, derived categories and functors
18-02 Research exposition (monographs, survey articles) pertaining to category theory
18G05 Projectives and injectives (category-theoretic aspects)
18G10 Resolutions; derived functors (category-theoretic aspects)
18G15 Ext and Tor, generalizations, Künneth formula (category-theoretic aspects)
18G20 Homological dimension (category-theoretic aspects)
18G35 Chain complexes (category-theoretic aspects), dg categories
18G40 Spectral sequences, hypercohomology
13C10 Projective and free modules and ideals in commutative rings
13C11 Injective and flat modules and ideals in commutative rings
13C15 Dimension theory, depth, related commutative rings (catenary, etc.)
13D05 Homological dimension and commutative rings
13D15 Grothendieck groups, \(K\)-theory and commutative rings
13D25 Complexes (MSC2000)
13E05 Commutative Noetherian rings and modules
13E10 Commutative Artinian rings and modules, finite-dimensional algebras
13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
13G05 Integral domains
13H05 Regular local rings
16Gxx Representation theory of associative rings and algebras
16Exx Homological methods in associative algebras
16D40 Free, projective, and flat modules and ideals in associative algebras
16P60 Chain conditions on annihilators and summands: Goldie-type conditions
16D50 Injective modules, self-injective associative rings
20J05 Homological methods in group theory


Zbl 0222.18003