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Model Theoretic Algebra With Particular Emphasis on Fields, Rings, Modules
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.
1101427654
Model Theoretic Algebra With Particular Emphasis on Fields, Rings, Modules
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.
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Model Theoretic Algebra With Particular Emphasis on Fields, Rings, Modules

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

by Christian.U Jensen
Model Theoretic Algebra With Particular Emphasis on Fields, Rings, Modules
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Model Theoretic Algebra With Particular Emphasis on Fields, Rings, Modules

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

by Christian.U Jensen

Overview

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.

Product Details

ISBN-13: 9781351431118
Publisher: CRC Press
Publication date: 03/10/2022
Series: Algebra, Logic and Applications
Sold by: Barnes & Noble
Format: eBook
Pages: 464
File size: 1 MB

About the Author

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

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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