This textbook, set for a one or two semester course in commutative algebra, provides an introduction to commutative algebra at the postgraduate and research levels. The main prerequisites are familiarity with groups, rings and fields. Proofs are self-contained.The book will be useful to beginners and experienced researchers alike. The material is so arranged that the beginner can learn through self-study or by attending a course. For the experienced researcher, the book may serve to present new perspectives on some well-known results, or as a reference.
The text covers in a reasonable number of pages a wealth of important topics of commutative algebra. Each section contains illustrative examples and is followed by a set of exercises. The text is suitable for graduate and postgraduate students, as well as for experienced researchers interested in commutative algebra. -- Mathematical Reviews "Mathematical Reviews"
Rings and Ideals; Modules and Algebras; Polynomials and Power Series Rings; Homological Tools I; Finiteness Conditions; Primary Decomposition; Filtrations and Completion; Numerical Functions; Dimension of Local Rings; Integral Extensions; Normal Domains; Integral Closure in a Finite Field Extension; Transcendental Extensions; Affine and Graded Rings; Valuation Rings and Valuations; Derivations and Differentials; Homological Tools II; Depth and Cohen-Macaulay Rings; Regular Rings; Divisor Class Groups.