Model theoretic algebra : with particular emphasis on fields, rings, modules
著者
書誌事項
Model theoretic algebra : with particular emphasis on fields, rings, modules
（Algebra, logic and applications series, v. 2）
Gordon and Breach Science Publishers, c1989
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注記
Bibliography: p. 411-427
Includes indexes
内容説明・目次
内容説明
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.
目次
- 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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