Commutative Rings: Dimension, Multiplicity and Homological Methods (Ellis Horwood Series in Mathematics & Its Applications)

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9780131556232: Commutative Rings: Dimension, Multiplicity and Homological Methods (Ellis Horwood Series in Mathematics & Its Applications)

This publication completes the comprehensive coverage of commutative ring theory begun in Balcerzyk and Jozefiak's "Commutative Noetherian and Krull Rings" (Ellis Horwood Limited, March 1989). This volume features the application of homological algebra to purely ring-theoretic problems, including an example of the homologous characterisation of regular local rings as local rings of finite global dimension. It describes the intersection multiplicity in terms of Tor functions, the characterisation of the depth of an ideal in terms of Ext functors, as well as local Gorenstein rings of finite injective dimension. The chapters incorporate exercises, the more difficult being furnished with hints. They are also enhanced by short notes and references which trace the methods and theorems of each chapter to its source. The text will be of interest to researchers and students of mathematics, algebra, commutative rings, algebraic geometry and algebraic number theory.

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