---

＜電子ブック＞
A Primer of Subquasivariety Lattices / by Kira Adaricheva, Jennifer Hyndman, J. B. Nation, Joy N. Nishida
(CMS/CAIMS Books in Mathematics. ISSN:27306518 ; 3)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
本文言語	英語
大きさ	IX, 290 p. 136 illus., 64 illus. in color : online resource
著者標目	*Adaricheva, Kira author Hyndman, Jennifer author Nation, J. B author Nishida, Joy N author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Universal algebra FREE:Order, Lattices, Ordered Algebraic Structures FREE:General Algebraic Systems
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-030-98088-7

 類似資料