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 axiom...
| Main Authors: | , |
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
[Place of publication not identified] :
Routledge,
2022.
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| Edition: | First edition. |
| Series: | Algebra, logic, and applications ;
v. 2. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic 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.