| Dewey Class |
511.33 |
| Title |
A Primer of Subquasivariety Lattices ( EBook/) / by Kira Adaricheva, Jennifer Hyndman, J. B. Nation, Joy N. Nishida. |
| Author |
Adaricheva, Kira |
| Added Personal Name |
Hyndman, Jennifer |
| Nation, J. B. |
| Nishida, Joy N. |
| Other name(s) |
SpringerLink (Online service) |
| Edition statement |
1st ed. 2022. |
| Publication |
Cham : : Springer International Publishing : : Imprint: Springer, , 2022. |
| Physical Details |
IX, 290 p. 136 illus., 64 illus. in color. : online resource. |
| Series |
CMS/CAIMS Books in Mathematics 2730-6518 ; ; 3 |
| ISBN |
9783030980887 |
| Summary Note |
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.: |
| Contents note |
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. |
| Mode of acces to digital resource |
Digital reproduction.- |
| Cham : |
| Springer International Publishing, |
| 2022. - |
| Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
https://doi.org/10.1007/978-3-030-98088-7 |
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