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Model Theory and Modules by M. Prest (Paperback, 1988)

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This self-contained introduction to the subject introduces the requisite model theory and module theory as it is needed. Later chapters discuss stability-theoretic aspects of modules, and structure and classification theorems over various types of rings and for certain classes of modules.

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Professor Prest is the first to address the topic of the development of the interplay between model theory and the theory of modules. In recent years the relationship between model theory and other branches of mathematics has led to many profound and intriguing results. This self-contained introduction to the subject introduces the requisite model theory and module theory as it is needed. It then develops the basic ideas of determining what can be said about modules using the information that may be expressed in first-order language. Later chapters discuss stability-theoretic aspects of modules, and structure and classification theorems over various types of rings and for certain classes of modules.