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A Primer of Subquasivariety Lattices

Record Type:	Language materials, printed : Monograph/item
Title/Author:	A Primer of Subquasivariety Lattices/ by Kira Adaricheva, Jennifer Hyndman, J. B. Nation, Joy N. Nishida.
Author:	Adaricheva, Kira.
other author:	Hyndman, Jennifer.
Description:	IX, 290 p. 136 illus., 64 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Algebra. -
Online resource:	https://doi.org/10.1007/978-3-030-98088-7
ISBN:	9783030980887

A Primer of Subquasivariety Lattices
Adaricheva, Kira.

A Primer of Subquasivariety Lattices[electronic resource] /by Kira Adaricheva, Jennifer Hyndman, J. B. Nation, Joy N. Nishida. - 1st ed. 2022. - IX, 290 p. 136 illus., 64 illus. in color.online resource. - CMS/CAIMS Books in Mathematics,32730-6518 ;. - CMS/CAIMS Books in Mathematics,1.

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(��), Γ) -- Lattices 1 + L as Lq(��) -- Representing distributive dually algebraic lattices -- Problems and an advertisement -- Appendices.

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.

ISBN: 9783030980887

Standard No.: 10.1007/978-3-030-98088-7doiSubjects--Topical Terms:

579870
Algebra.

LC Class. No.: QA150-272

Dewey Class. No.: 511.33

A Primer of Subquasivariety Lattices
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505 0 $a 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(��), Γ) -- Lattices 1 + L as Lq(��) -- Representing distributive dually algebraic lattices -- Problems and an advertisement -- Appendices.
520 $a 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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