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This book is intended as a reference for mathematicians working with homological dimensions in commutative algebra and as an introduction to Gorenstein dimensions for graduate students with an interest in the same. Any admirer of classics like the Auslander-Buchsbaum-Serre characterization of regular rings, and the Bass and Auslander-Buchsbaum formulas for injective and projective dimension of f.g. modules will be intrigued by this book's content. Readers should be well-versed in commutative algebra and standard applications of homological methods. The framework is that of complexes, but all major results are restated for modules in traditional notation, and an appendix makes the proofs accessible for even the casual user of hyperhomological methods.

Gorenstein rings. --- Gorenstein Rings --- Homologie --- Homology theory --- Homology theory. --- Algebra. --- K-theory. --- Mathematics. --- K-Theory. --- Mathematics, general. --- Math --- Science --- Algebraic topology --- Mathematics --- Mathematical analysis

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The notions of torsion and torsion freeness have played a very important role in module theory--particularly in the study of modules over integral domains. Furthermore, the use of homological techniques in this connection has been well established. It is the aim of this paper to extend these techniques and to show that this extension leads naturally to several new concepts (e.g. k-torsion freeness and Gorenstein dimension) which are useful in the classification of modules and rings.

Ordered algebraic structures --- Modules (Algebra) --- Modules (algèbre) --- Torsion theory (Algebra) --- Torsion, Théorie de la (algèbre) --- Homology theory --- Cohomologie. --- Homologie. --- Rings (Algebra) --- Anneaux (algèbre) --- Noetherian rings. --- Gorenstein rings. --- Commutative rings. --- Modules (Algebra). --- Rings (Algebra).