ABSTRACT

This volume highlights the links between model theory and algebra. The work contains a definitive account of algebraically compact modules, a topic of central importance for both module and model theory. Using concrete examples, particular emphasis is given to model theoretic concepts, such as axiomizability. Pure mathematicians, especially algebraists, ring theorists, logicians, model theorists and representation theorists, should find this an absorbing and stimulating book.

chapter Chapter 1|9 pages

Introduction. Ultraproducts. Definitions and examples

chapter Chapter 4|14 pages

Peano rings and Peano fields

chapter Chapter 6|34 pages

The language of modules over a fixed ring

chapter Chapter 7|36 pages

Algebraically compact modules

chapter Chapter 8|63 pages

Decompositions and algebraic compactness

chapter Chapter 10|33 pages

The first order theory of rings

chapter Chapter 11|23 pages

Pure global dimension and algebraically compact rings

chapter Chapter 12|46 pages

Representation theory of finite dimensional algebras

chapter Chapter 13|7 pages

Problems

chapter |9 pages

Tables