Model Theoretic Algebra With Particular Emphasis on Fields, Rings, Modules  book cover
1st Edition

Model Theoretic Algebra With Particular Emphasis on Fields, Rings, Modules

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ISBN 9782881247170
Published July 26, 1989 by CRC Press
458 Pages

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Book Description

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.

Table of Contents

Introduction, ultraproducts, definitions and examples; elementary equivalence - axiomatizable and finitely axiomatizable classes - examples and results in field theory; elementary definability - applications to polynomial and power series rings and their quotient fields; peano rings and peano fields; hilbertian fields and realizations of finite groups as galois groups; the language of modules over a fixed ring; algebraically compact modules; decompositions and algebraic compactness; the two sorted language of modules over unspecified rings; the first order theory of rings; pure global dimension and algebraically compact rings; representation theory of finite dimensional algebras; problems; tables; basic notions and definitions from homological algebra; functor categories on finitely presented modules.

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Christian. U Jensen (University of Copenhagen, Denmark) (Author) , Helmt Lenzing (Paderborn University, Germany) (Author)