Roots of Ext, their abstract elementary classes, deconstruction, and applications

Abstract

We survey the tools expressing roots of the Ext functor as transfinite extensions of small roots (where small = countably or finitely generated), and study the related AECs in the sense of Shelah. Applications include a new proof of the Bazzoni-Herbera characterization of modules of projective dimension at most one over semiprime Goldie rings.

Keywords

• Roots
• their
• abstract
• elementary
• classes
• deconstruction
• applications