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Ordered algebraic structures --- Commutative rings --- 512.71 --- Rings (Algebra) --- Commutative rings and algebras. Local theory. Foundations of algebraic geometry --- Commutative rings. --- 512.71 Commutative rings and algebras. Local theory. Foundations of algebraic geometry

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Ordered algebraic structures --- Commutative rings. --- 512.71 --- Commutative rings --- Rings (Algebra) --- Commutative rings and algebras. Local theory. Foundations of algebraic geometry --- 512.71 Commutative rings and algebras. Local theory. Foundations of algebraic geometry

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512.71 --- 512.55 --- Commutative rings and algebras. Local theory. Foundations of algebraic geometry --- Rings and modules --- 512.55 Rings and modules --- 512.71 Commutative rings and algebras. Local theory. Foundations of algebraic geometry --- Algèbres commutatives

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In addition to being an interesting and deep subject in its own right, commutative ring theory is important as a foundation for algebraic geometry and complex analytic geometry. This graduate textbook covers the basic material, including dimension theory, depth, Cohen-Macaulay rings, Gorenstein rings, Krull rings and valuation rings, but it is distinguished from other introductions by the coverage of advanced topics such as Ratliff's theorems on chains of prime ideals. The work is essentially self-contained, the only prerequisite being a sound knowledge of modern algebra, yet the reader is taken to the frontiers of the subject. Exercises are provided at the end of each section and solutions or hints to some of them are given at the end of the book. Consequently it can be used by graduate students taking courses in commutative algebra, algebraic geometry or complex analytic geometry, but will also serve as an introduction to these subjects for non-specialists.

Commutative rings --- 512.71 --- Rings (Algebra) --- 512.71 Commutative rings and algebras. Local theory. Foundations of algebraic geometry --- Commutative rings and algebras. Local theory. Foundations of algebraic geometry --- Commutative rings.

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Ordered algebraic structures --- 512.71 --- Commutative rings --- Dimension theory (Algebra) --- Homology theory --- Cohomology theory --- Contrahomology theory --- Algebraic topology --- Associative algebras --- Commutative algebra --- Rings (Algebra) --- Commutative rings and algebras. Local theory. Foundations of algebraic geometry --- Commutative rings. --- Homology theory. --- Dimension theory (Algebra). --- 512.71 Commutative rings and algebras. Local theory. Foundations of algebraic geometry