1st Edition
Compatibility, Stability, and Sheaves
Integrates fundamental techniques from algebraic geometry, localization theory and ring theory, and demonstrates how each topic is enhanced by interaction with others, providing new results within a common framework. Technical conclusions are presented and illustrated with concrete examples.
Preface
Localization
Localization at multiplicative subsets
Radicals
Localization
Symmetric radicals
Associated primes
The second layer condition
FBN rings
Extensions
Centralizing extensions
Normalizing extensions
Strongly normalizing extensions
Inducing radicals
Inducing localization functors
Functorial behaviour
Extensions and localization at prime ideals
Stability
Stable torsion theories
The Artin-Rees property
The weak Artin-Rees property
Biradicals
Compatibility and Sheaves
Sheaves
The commutative theory
Compatibility in module categories
Topologies
Structure sheaves
Bibliography
Index
Biography
J.L. Bueso
". . .a good and worthwhile summation of the current status of [the ideal-theoretic spectrum] approach, which is of definitive value for researchers wishing to enter the area or make use of its results. "
---Mathematical Reviews
