A Primer of Subquasivariety Lattices

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Synopsis

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.

Book details

Edition:
1st ed. 2022
Series:
CMS/CAIMS Books in Mathematics (Book 3)
Author:
Kira Adaricheva, Jennifer Hyndman, J. B. Nation, Joy N. Nishida
ISBN:
9783030980887
Related ISBNs:
9783030980870
Publisher:
Springer International Publishing
Pages:
N/A
Reading age:
Not specified
Includes images:
Yes
Date of addition:
2022-09-02
Usage restrictions:
Copyright
Copyright date:
2022
Copyright by:
The Editor 
Adult content:
No
Language:
English
Categories:
Mathematics and Statistics, Nonfiction