Model Theoretic Algebra With Particular Emphasis on Fields, Rings, Modules
1st Edition
Published on 10. March 2022
464 pages
978-1-351-43112-5 (ISBN)
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.
More details
Series
Edition
1. Auflage
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
Professional and scholarly
ISBN-13
978-1-351-43112-5 (9781351431125)
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Schweitzer Classification
Other editions
Additional editions
Christian.U Jensen
Model Theoretic Algebra With Particular Emphasis on Fields, Rings, Modules
Book
07/1989
1st Edition
Gordon & Breach Science Publishers SA
€861.64
Article not available at the moment
Persons
Christian. U Jensen (University of Copenhagen, Denmark) (Author) , Helmt Lenzing (Paderborn University, Germany) (Author)
Content
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.
