{"product_id":"model-theory-and-modules-paperback-9780521348331","title":"Model Theory and Modules (Paperback) 9780521348331","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eModel Theory and Modules\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eM. Prest (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521348331, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 25 February 1988\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e400 pages\u003cbr\u003e22.8 x 15.2 x 2.3 cm, 0.59 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"...contains a rich collection of concrete examples and exercises.  It may be useful both as a reference book and as a texbook.\"   Mathematical Reviews\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eIn recent years the interplay between model theory and other branches of mathematics has led to many deep and intriguing results. In this, the first book on the topic, the theme is the interplay between model theory and the theory of modules. The book is intended to be a self-contained introduction to the subject and introduces the requisite model theory and module theory as it is needed. Dr Prest develops the basic ideas concerning what can be said about modules using the information which may be expressed in a 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. Both algebraists and logicians will enjoy this account of an area in which algebra and model theory interact in a significant way. The book includes numerous examples and exercises and consequently will make an ideal introduction for graduate students coming to this subject for the first time.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction\u003cbr\u003e Acknowledgements\u003cbr\u003e Notations and conventions\u003cbr\u003e Remarks on the development of the area\u003cbr\u003e Section summaries\u003cbr\u003e 1. Some preliminaries\u003cbr\u003e 2. Positive primitive formulas and the sets they define\u003cbr\u003e 3. Stability and totally transcendental modules\u003cbr\u003e 4. Hulls\u003cbr\u003e 5. Forking and ranks\u003cbr\u003e 6. Stability-theoretic properties of types\u003cbr\u003e 7. Superstable modules\u003cbr\u003e 8. The lattice of pp-types and free realisations of pp-types\u003cbr\u003e 9. Types and the structure of pure-injective modules\u003cbr\u003e 10. Dimension and decomposition\u003cbr\u003e 11. Modules over artinian rings\u003cbr\u003e 12. Functor categories\u003cbr\u003e 13. Modules over artin algebras\u003cbr\u003e 14. Projective and flat modules\u003cbr\u003e 15. Torsion and torsionfree classes\u003cbr\u003e 16. Elimination of quantifiers\u003cbr\u003e 17. Decidability and undecidability\u003cbr\u003e Problems page\u003cbr\u003e Bibliography\u003cbr\u003e Examples index\u003cbr\u003e Notation index\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46007113777432,"sku":"9780521348331","price":67.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521348331i_3f3e533a-fc7d-4032-b0b2-8510b9657b9f.jpg?v=1691375530","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/model-theory-and-modules-paperback-9780521348331","provider":"Freshly Printed Books","version":"1.0","type":"link"}