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Iacob A. Gorenstein Homological Algebra

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Iacob A. Gorenstein Homological Algebra
CRC Press; Taylor & Francis Group, 2019. — 233 p. — ISBN-13 978-1-138-06549-9.
Gorenstein homological algebra is an important area of mathematics, with applications in commutative and noncommutative algebra, model category theory, representation theory, and algebraic geometry. While in classical homological algebra the existence of the projective, injective, and flat resolutions over arbitrary rings are well known, things are a little different when it comes to Gorenstein homological algebra. The main open problems in this area deal with the existence of the Gorenstein injective, Gorenstein projective, and Gorenstein flat resolutions. Gorenstein Homological Algebra is especially suitable for graduate students interested in homological algebra and its applications.
Contents
Modules – projective, injective, and flat modules
Gorenstein projective, injective, and flat modules
Gorenstein projective resolutions
Gorenstein injective resolutions
Gorenstein flat precovers and preenvelopes
Connections with Tate (co)homology
Totally acyclic complexes
Generalizations of the Gorenstein modules
Gorenstein projective, injective, flat complexes, dg-projective, dg-injective, dg-flat complexes
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