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ISBN: 9783030980887 9783030980870 9783030980894 9783030980900 Year: 2022 Publisher: Cham Springer International Publishing
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This book addresses Birkhoff and Mal'cev's problem of describing subquasivariety lattices. The text begins by developing the basics of atomic theories and implicational theories in languages that may, or may not, contain equality. Subquasivariety lattices are represented as lattices of closed algebraic subsets of a lattice with operators, which yields new restrictions on the equaclosure operator. As an application of this new approach, it is shown that completely distributive lattices with a dually compact least element are subquasivariety lattices. The book contains many examples to illustrate these principles, as well as open problems. Ultimately this new approach gives readers a set of tools to investigate classes of lattices that can be represented as subquasivariety lattices.
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ISBN: 9783030980887 Year: 2022 Publisher: Cham Springer International Publishing :Imprint: Springer
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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 --- 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
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