Title A primer of subquasivariety lattices / Kira Adaricheva, Jennifer Hyndman, J. B. Nation, Joy N. Nishida

Published Cham : Springer, 2022

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Description 1 online resource (ix, 290 pages) : illustrations (some color) Series CMS/CAIMS books in mathematics, 2730-6518 ; volume 3 CMS/CAIMS books in mathematics ; v. 3. 2730-6518 Contents Preface -- Introduction -- Varieties and quasivarieties in general languages -- Equaclosure operators -- Preclops on finite lattices -- Finite lattices as Sub(S,, 1): The case J(L) (L) -- Finite lattices as Sub(S,, 1): The case J(L) (L) -- The six-step program: From (L) to (Lq) -- Lattices 1 + L as Lq-- Representing distributive dually algebraic lattices -- Problems and an advertisement -- Appendices Summary 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 Bibliography Includes bibliographical references and indexes Notes Online resource; title from PDF title page (SpringerLink, viewed August 22, 2022) Subject Quasivarieties (Universal algebra) Álgebra Retículos, Teoría de Quasivarieties (Universal algebra) Varietats algebraiques. Àlgebra universal. Genre/Form Electronic books Llibres electrònics. Form Electronic book Author Hyndman, Jennifer (Mathematician), author. Nation, J. B. (James Bryant), 1948- author. Nishida, Joy N. author. ISBN 9783030980887 303098088X 9788303098085 830309808X

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