img Leseprobe Leseprobe

A Primer of Subquasivariety Lattices

Joy N. Nishida, Jennifer Hyndman, J. B. Nation, et al.

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ca. 96,29 €
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Springer International Publishing img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Arithmetik, Algebra

Beschreibung

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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Schlagwörter

relational structure, equational closure operator, variety, congruence, fully invariant congruence, lattice of subquasivarieties, dually algebraic lattice, quasivariety