Prest M. Model Theory and Modules

UK.: Cambridge University Press, 1988. — 388 p. — (London Mathematical Society Lecture Note Series. 130) - ISBN: 0-521-34833-1, English (OCR-Слой).Professor Prest is the first to address the topic of the development of the interplay between model theory and the theory of modules..
In recent years the relationship between model theory and other branches of mathematics has led to many profound and intriguing results. This self-contained introduction to the subject introduces the requisite model theory and module theory as it is needed. It then develops the basic ideas of determining what can be said about modules using the information that may be expressed in first-order language. Later chapters discuss stability-theoretic aspects of modules, and structure and classification theorems over various types of rings and for certain classes of modules.Acknowledgements.
Notations and conventions.
Remarks on the development of the area.
Section summaries.
Some preliminaries.
Positive primitive formulas and the sets they define.
Stability and totally transcendental modules.
Hulls.
Forking and ranks.
Stability-theoretic properties of types.
Superstable modules.
The lattice of pp-types and free realisations of pp-types.
Types and the structure of pure-injective modules.
Dimension and decomposition.
Modules over artinian rings.
Functor categories.
Projective and flat modules.
Torsion and torsionfree classes.
Elimination of quantifiers.
Decidability and undecidability.
Problems page.Examples index.
Notation index.