The Algebraic Theory of Modular Systems
by Francis Sowerby Macaulay
Publisher: Cambridge University Press 1916
Number of pages: 140
Many of the ideas introduced by F.S. Macaulay in this classic book have developed into central concepts in what has become the branch of mathematics known as Commutative Algebra. Today his name is remembered through the term 'Cohen-Macaulay ring'.
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by Steven V Sam, Andrew Snowden - arXiv
An expository account of the theory of twisted commutative algebras, which can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate rings of determinantal varieties, etc.
by David Eisenbud, et al. - Cambridge University Press
The books cover birational geometry, D-modules, invariant theory, matrix factorizations, noncommutative resolutions, singularity categories, support varieties, tilting theory, etc. These volumes reflect the lively interaction between the subjects.
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 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.