by Pete L. Clark
Publisher: University of Georgia 2015
Number of pages: 363
Contents: Introduction to Commutative Rings; Introduction to Modules; Ideals; Examples of Rings; Swan's Theorem; Localization; Noetherian Rings; Boolean rings; Affine algebras and the Nullstellensatz; The spectrum; Integral extensions; Factorization; Dedekind domains; Picard groups.
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by J.S. Milne
These notes prove the basic theorems in commutative algebra required for algebraic geometry and algebraic groups. They assume only a knowledge of the algebra usually taught in advanced undergraduate or first-year graduate courses.
by Ezra Miller - arXiv
This is a survey of lattice point methods for binomial ideals. It is aimed at students and researchers in algebra; it includes many examples, open problems, and elementary introductions to the motivations and background from outside of algebra.
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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.
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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'.