Model Theoretic Algebra With Particular Emphasis On Fields Rings Modules
Download Model Theoretic Algebra With Particular Emphasis On Fields Rings Modules PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Model Theoretic Algebra With Particular Emphasis On Fields Rings Modules book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Model Theoretic Algebra With Particular Emphasis on Fields, Rings, Modules
Looks like a text (and a handsome one at that), but the authors prefer to describe their creation as "notes", intended to acquaint graduate students with "the power of the most basic principles of model theory by applying them to classical questions in algebra". Thirteen chapters (the last given to the enumeration of some open problems), plus tables and several appendices, bibliography. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
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.
Introduction to Model Theory
Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct technique (rather than via the completeness theorem of first-order logic). This leads fairly quickly to algebraic applications, like Malcev's local theorems of group theory and, after a little more preparation, to Hilbert's Nullstellensatz of field theory. Steinitz dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.