Primer of Subquasivariety Lattices

AvKira Adaricheva,Jennifer Hyndman

Häftad, Engelska, 2023

Del 3 i serien CMS/CAIMS Books in Mathematics

976 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt över 249 kr.

Fler format och utgåvor

Inbunden

1 407 kr

Beskrivning

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.

Produktinformation

Utgivningsdatum:2023-08-20
Mått:155 x 235 x 17 mm
Vikt:458 g
Format:Häftad
Språk:Engelska
Serie:CMS/CAIMS Books in Mathematics
Antal sidor:290
Förlag:Springer Nature Switzerland AG
ISBN:9783030980900

Utforska kategorier

Algebra inom Naturvetenskap och teknik

Recensioner i media

“This is a research monograph that reports on investigations, both classical and new, into the structure of subquasivariety lattices. ... This monograph is a study of the structure of lattices of the form Lq(K). In this monograph, relation symbols are permitted. ... The monograph spans 290 pages and has 10 chapters and three appendices.” (Keith A. Kearnes, Mathematical Reviews, April, 2024)

Innehållsförteckning

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.