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Introduction to Commutative Algebra by Jason McCullough
This note covers the following topics, Primary Decomposition, Filtrations and Completions, Dimension Theory, Integral Extensions, Homological Methods, Depth and Cohen Macaulay Modules, Injective Modules over Noetherian Rings, Local Cohomology, Applications and Generalizations.
Author(s): Jason McCullough
268 Pages 
Frobenius Splitting in Commutative Algebra
This note contains below topics, The Frobenius Map for Rings the local theory, Frobenius for Schemes the Global Theory, The Test Ideal, Test Ideals for Pairs, So what does CohenMacaulay mean.
Author(s): Karen E. Smith, Wenliang Zhang
53 Pages
Introduction to Commutative Algebra by Jason McCullough
This note covers the following topics, Primary Decomposition, Filtrations and Completions, Dimension Theory, Integral Extensions, Homological Methods, Depth and Cohen Macaulay Modules, Injective Modules over Noetherian Rings, Local Cohomology, Applications and Generalizations.
Author(s): Jason McCullough
268 Pages
Introduction to commutative Algebra Lecture Notes
This Lecture note contains the following topics, Prime ideals and localization, Finite and integral homomorphisms, Noetherian rings and modules, Associated Primes and primary decomposition, Noether normalization, Nullstellensatz and the maximal spectrum, Dimension theory, special cases of rings, Tor and Ext, Flatness, Depth and Cohen Macaulay rings and Modules, Regular rings and Graded modules.
Author(s): Mircea Mustata, Department of University of Michigan
92 Pages
This book is a clear, concise, and efficient textbook, aimed at beginners, with a good selection of topics. Topics covered includes, Rings and Ideals, Radicals, Filtered Direct Limits, CayleyHamilton Theorem, Localization of Rings and Modules, KrullCohenSeidenberg Theory, Rings and Ideals, Direct Limits, Filtered direct limit.
Author(s): Allen Altman and Steven Kleiman
266 Pages