Commutative Algebra and Noncommutative Algebraic Geometry
by David Eisenbud, et al.
Publisher: Cambridge University Press 2015
Number of pages: 775
The books cover birational geometry, D-modules, invariant theory, matrix factorizations, noncommutative resolutions, singularity categories, support varieties, tilting theory, etc. These two volumes reflect the lively interaction between the subjects.
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by Sudhir R. Ghorpade - Indian Institute of Technology, Bombay
These notes give a rapid review of the rudiments of classical commutative algebra. Some of the main results whose proofs are outlined here are: Hilbert basis theorem, primary decomposition of ideals in noetherian rings, Krull intersection theorem.
by Luchezar L. Avramov, at al. - Cambridge University Press
This book focuses on the interaction of commutative algebra with other areas of mathematics, including algebraic geometry, group cohomology and representation theory, and combinatorics, with all necessary background provided.
by Robert B. Ash - University of Illinois
This is a text for a basic course in commutative algebra, it should be accessible to those who have studied algebra at the beginning graduate level. The book should help the student reach an advanced level as quickly and efficiently as possible.
by Karen E. Smith, Wenliang Zhang - arXiv
Frobenius splitting has inspired a vast arsenal of techniques in commutative algebra, algebraic geometry, and representation theory. The purpose of these lectures is to give a gentle introduction to Frobenius splitting for beginners.