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ISBN: 3319782347 3319782355 Year: 2018 Publisher: Cham : Springer International Publishing : Imprint: Springer,
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This book discusses the ways in which the algebras in a locally finite quasivariety determine its lattice of subquasivarieties. The book starts with a clear and comprehensive presentation of the basic structure theory of quasivariety lattices, and then develops new methods and algorithms for their analysis. Particular attention is paid to the role of quasicritical algebras. The methods are illustrated by applying them to quasivarieties of abelian groups, modular lattices, unary algebras and pure relational structures. An appendix gives an overview of the theory of quasivarieties. Extensive references to the literature are provided throughout.
Quasivarieties (Universal algebra) --- 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 --- Algorithms. --- Algebra. --- Mathematics --- Mathematical analysis --- Algorism --- Algebra --- Arithmetic --- Foundations
ISBN: 1280312327 9786610312320 0387275703 038727569X 1441939016 Year: 2005 Publisher: New York ; [London] : Springer,
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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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ISBN: 3030980871 303098088X Year: 2022 Publisher: Cham, Switzerland : Springer,
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Quasivarieties (Universal algebra) --- 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 --- Varietats algebraiques --- Àlgebra universal --- Àlgebra --- Àlgebra lineal --- Anàlisi vectorial --- Categories (Matemàtica) --- Matrius (Matemàtica) --- Quaternions --- Nombres complexos --- Varietats algèbriques --- Geometria algebraica --- Varietats tòriques --- Grups algebraics lineals
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