Description
Gorenstein Homological Algebra
Author: Iacob Alina
Language: English
Subjects for Gorenstein Homological Algebra:
Keywords
Gorenstein Projective; Gorenstein Flat; injective resolutions; Cotorsion Pair; projective; injective and flat complexes; Gorenstein Flat Modules; projective modules; Gorenstein Injective Modules; non-coherent rings; Complete Hereditary Cotorsion Pair; tate cohomology; Finite Gorenstein Projective Dimension; model category theory; Noetherian Ring; representation theory; Gorenstein Projective Modules; noncommutative algebra; Finite Flat Dimension; Gorenstein homological algebra; Finite Projective Dimension; algebraic geometry; Complete Cotorsion Pair; Triangulated Category; Acyclic Complex; Direct Summand; Gorenstein Projective Dimension; Pure Quotients; FP Injective Dimension; Commutative Noetherian Rings; Gorenstein Ring; Short Exact Sequence; Pure Submodules; Exact Complex; Left Coherent Ring
· 15.6x23.4 cm · Hardback
Description
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/li>Biography
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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.
Introduction. Preliminaries. Gorenstein projective, Gorenstein injective and Gorenstein flat modules. Gorenstein projective resolutions. Gorenstein injective resolutions. Gorenstein flat precovers and preenvelopes. Connections with Tate (co)homology, Tate-Betti and Tate-Bass numbers. Applications to the category of complexes. Totally acyclic complexes.
Alina Iacob is a professor of mathematics at Georgia Southern University. Her primary research interests are homological and communicative algebra.
