Model theory and modules

Prest, Mike (2003) Model theory and modules. In: Handbook of Algebra. Elsevier, pp. 227-253. ISBN 0-444-51264-0

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Abstract

The model-theoretic investigation of modules has led to ideas, techniques and results which are of algebraic interest, irrespective of their model-theoretic significance. It is these aspects that I will discuss in this article, although I will make some comments on the model theory of modules per se. Our default is that the term “module” will mean (unital) right module over a ring (associative with 1) R. The category of such modules is denoted Mod-R, the full subcategory of finitely presented modules will be denoted mod-R, the notation R-Mod denotes the category of left R-modules. By Ab we mean the category of abelian groups. In Part 1 we introduce the general concepts and in Part 2 we discuss these in more specific contexts. References within the text, as well as those in the bibliography, are neither complete nor comprehensive but are intended to lead the reader to a variety of sources

Item Type: Book Section
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations
MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras
Depositing User: Professor Mike Prest
Date Deposited: 22 May 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/281

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