Gorenstein Homological Algebra / by Alina Iacob.
Material type:
TextLanguage: English Publisher: Boca Raton, FL : CRC Press, an imprint of Taylor and Francis, 2018Edition: 1st editionDescription: 1 online resource (232 pages) : 55 illustrations, text file, PDFContent type: text Media type: computer Carrier type: online resourceISBN: 9781315159676Subject(s): MATHEMATICS / Geometry / General | MATHEMATICS / Number Theory | Algebra, HomologicalGenre/Form: Electronic books.Additional physical formats: Print version: : No titleDDC classification: 512/.64 LOC classification: QA169 | .I23 2018Online resources: Click here to view. Also available in print format.Includes bibliographical references and index.
Foreword -- Preface -- 1 Modules - projective, injective, at modules -- 2 Gorenstein projective, injective and at modules -- 3 Gorenstein projective resolutions -- 4 Gorenstein injective resolutions -- 5 Gorenstein at precovers and preenvelopes -- 6 Connections with Tate (co)homology -- 7 Totally acyclic complexes -- 8 Generalizations of the Gorenstein modules -- 9 Gorenstein projective, injective, at complexes, dg-projective, dg-injective, dg-at complexes
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.
Also available in print format.