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 Jacob Lurie, Akhil Mathew - Harvard University
Topics: Unique factorization; Basic definitions; Rings of holomorphic functions; R-modules; Ideals; Localization; SpecR and Zariski topology; The ideal class group; Dedekind domains; Hom and the tensor product; Exactness; Projective modules; etc.
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.
This wikibook is intended to give an introduction to commutative algebra; i.e. it shall comprehensively describe the most important commutative algebraic objects. The axiom of choice will be used, although there is no indication that it is true.
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.