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