Document Zbl 0441.18018

An introduction to homological algebra. (English) Zbl 0441.18018

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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

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