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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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This monograph first published in 1986 is a reasonably self-contained account of a large part of the theory of non-commutative Noetherian rings. The author focuses on two important aspects: localization and the structure of infective modules. The former is presented in the opening chapters after which some new module-theoretic concepts and methods are used to formulate a new view of localization. This view, which is one of the book's highlights, shows that the study of localization is inextricably linked to the study of certain injectives and leads, for the first time, to some genuine applications of localization in the study of Noetherian rings. In the last part Professor Jategaonkar introduces a unified setting for four intensively studied classes of Noetherian rings: HNP rings, PI rings, enveloping algebras of solvable Lie algebras, and group rings of polycyclic groups. Some appendices summarize relevant background information about these four classes.

Noetherian rings. --- Localization theory. --- Categories (Mathematics) --- Homotopy theory --- Nilpotent groups --- Rings, Noetherian --- Associative rings --- Commutative rings

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Noetherian rings --- Localization theory --- Ordered algebraic structures --- 512.55 --- Rings, Noetherian --- Associative rings --- Commutative rings --- Categories (Mathematics) --- Homotopy theory --- Nilpotent groups --- 512.55 Rings and modules --- Rings and modules --- Anneaux noethériens. --- Noetherian rings. --- Algèbres associatives --- Algèbres associatives --- Anneaux noethériens.