Gorenstein Homological Algebra

1. Auflage 2018
ISBN: 978-1-138-06549-9
Verlag: CRC Press

Buch, Englisch, 232 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 520 g

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.

Autoren/Hrsg.

Iacob, Alina

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

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.

Über Autor(innen)

Alina Iacob is a professor of mathematics at Georgia Southern University. Her primary research interests are homological and communicative algebra.