A Course In Commutative Algebra
by Robert B. Ash
Publisher: University of Illinois 2006
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.
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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.
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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.
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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; etc.