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2006.112: Model theory and modules

2006.112: Mike Prest (2003) Model theory and modules. In: M Hazewinkel, (eds). Handbook of Algebra. Elsevier, pp. 227-253. ISBN 0-444-51264-0

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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 2000 > 03 Mathematical logic and foundations
MSC 2000 > 16 Associative rings and algebras
MIMS number:2006.112
Deposited By:Professor Mike Prest
Deposited On:22 May 2006

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