Presents a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality. This book describes Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it.

This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We ...

An introduction, suitable for beginning graduate students, showing connections to other areas of mathematics.

A graduate text covering Grothendieck's local cohomology theory.

Focuses on the basic mathematical tools needed for cryptographic design: computational difficulty (one-way functions), pseudorandomness and zero-knowledge proofs.

This book presents an account of several conjectures arising in commutative algebra from the pioneering work of Serre and Auslander-Buchsbaum.