A Primer of Subquasivariety Lattices
by Kira Adaricheva, Jennifer Hyndman, J. B. Nation, Joy N. Nishida
- Resource Type:
- E-Book
- Edition:
- 1st ed. 2022
- Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2022
- Related Series:
More Details
- 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.
- Table of 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( ), Γ)
- Lattices 1 + L as Lq( )
- Representing distributive dually algebraic lattices
- Problems and an advertisement
- Appendices.
- Author/Creator:
- Adaricheva, Kira , author
- Contributors:
- Hyndman, Jennifer , authorNation, J. B , authorNishida, Joy N , author
- Languages:
- English
- Language Notes:
- Item content: English
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- Subjects:
- Physical Description:
- IX, 290 pages 136 illustrations, 64 illustrations in color : online resource.
- Digital Characteristics:
- text file
- ISBNs:
- 9783030980887
9788303098085 (7) - Other Standard Numbers:
- Digital Object Identifier: 10.1007/978-3-030-98088-7
- OCLC Numbers:
- 1374611745