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Natural duality theory is one of the major growth areas within general algebra. This text provides a short path to the forefront of research in duality theory. It presents a coherent approach to new results in the area, as well as exposing open problems. Unary algebras play a special role throughout the text. Individual unary algebras are relatively simple and easy to work with. But as a class they have a rich and complex entanglement with dualisability. This combination of local simplicity and global complexity ensures that, for the study of natural duality theory, unary algebras are an excellent source of examples and counterexamples. A number of results appear here for the first time. In particular, the text ends with an appendix that provides a new and definitive approach to the concept of the rank of a finite algebra and its relationship with strong dualisability. Audience This book is intended for established researchers in natural duality theory, general algebraists wishing to commence research in duality theory, and graduate students in algebra.
Unary algebras. --- Quasivarieties (Universal algebra) --- Duality theory (Mathematics) --- Algebra --- Mathematical analysis --- Topology --- Algebraic systems, Quasi-varieties of --- Classes, Implicationally defined --- Classes, Quasi-primitive --- Classes, Universal Horn --- Horn classes, Universal --- Implicationally defined classes --- Quasi-primitive classes --- Quasi-varieties of algebraic systems --- Quasiprimitive classes --- Universal Horn classes --- Varieties (Universal algebra) --- Logic, Symbolic and mathematical --- Algebra, Universal --- Algebraic functions --- Algebra. --- Combinatorics. --- General Algebraic Systems. --- Order, Lattices, Ordered Algebraic Structures. --- Science, Humanities and Social Sciences, multidisciplinary. --- Combinatorics --- Mathematics --- Ordered algebraic structures. --- Algebraic structures, Ordered --- Structures, Ordered algebraic
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This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures.
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Agriculture and state --- Agriculture --- Congresses --- Economic aspects --- European Economic Community --- 631.15 <41> --- European Union --- -Agriculture and state --- -Agrarian question --- Agricultural policy --- State and agriculture --- Economic policy --- Land reform --- Farming --- Husbandry --- Industrial arts --- Life sciences --- Food supply --- Land use, Rural --- Farm production. Farm management. Farm administration--Verenigd Koninkrijk van Groot-Brittannië en Noord-Ierland --- Congresses. --- -Congresses --- Government policy --- -Farm production. Farm management. Farm administration--Verenigd Koninkrijk van Groot-Brittannië en Noord-Ierland --- 631.15 <41> Farm production. Farm management. Farm administration--Verenigd Koninkrijk van Groot-Brittannië en Noord-Ierland --- -Farming --- Agrarian question --- Economic aspects&delete& --- CEE --- Evropeĭskiĭ Soi︠u︡z --- C.E.E. --- Communauté économique européenne --- Comunidad Económica Europea --- Comunità economica europea --- EEC --- EC --- Europäische Wirtschaftsgemeinschaft --- Europejska Wspólnota Gospodarcza --- Europese Economische Gemeenschap --- Európai Gazdasági Közösség --- EHS --- Kurapʻa Kyŏngje Kongdongchʻe --- Kurapʻa Kongdong Sijang --- EEG --- Evropeĭska ikonomicheska obshtnost --- Evropské hospodářské spolecenstvi --- Comunidade Económica Europeia --- EWG --- Europæiske økonomiske fællesskab --- EØF --- Koinē Agora --- EOK --- MCE --- Mercado Común Europeo --- Europeiske økonomiske fellesskap --- Evropeĭskoe ėkonomicheskoe soobshchestvo --- MEC --- Evropska ekonomska zaednica --- EZZ --- Common Market --- Marché commun --- EĖS --- Avrupa Ekonomik Topluluğu --- AET --- Müşterek Pazar --- Ortak Pazar --- Sūq al-Ūrūbbīyah al-Mushtarakah --- Mercado Comum --- Europaikē Oikonomikē Koinotēta --- Evropska gospodarska skupnost --- Mercato comune --- EEZ --- Evropska ekonomska zajednica --- Euroopan Yhteisö --- EY --- EIO --- Shuḳ ha-Eropi ha-meʼuḥad --- Suq Komuni --- Eurōpaïkē Koinotēta --- Comunidade Européia --- Mercado Comum Europeau --- Unia Europejska --- Koinotēta --- E.G. --- קהילה האירופית --- קהילייה האירופאית --- שוק הארופאי המשותף --- Evropeisku Félagsmarknaðin --- EF --- CEE (European Economic Community) --- C.E.E. (European Economic Community) --- EEC (European Economic Community)
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