NDLI: Generalized Priestley Quasi-Orders

Content Provider	Springer Nature Link
Author	Bezhanishvili, Guram Jansana, Ramon
Copyright Year	2010
Abstract	We introduce generalized Priestley quasi-orders and show that subalgebras of bounded distributive meet-semilattices are dually characterized by means of generalized Priestley quasi-orders. This generalizes the well-known characterization of subalgebras of bounded distributive lattices by means of Priestley quasi-orders (Adams, Algebra Univers 3:216–228, 1973; Cignoli et al., Order 8(3):299–315, 1991; Schmid, Order 19(1):11–34, 2002). We also introduce Vietoris families and prove that homomorphic images of bounded distributive meet-semilattices are dually characterized by Vietoris families. We show that this generalizes the well-known characterization (Priestley, Proc Lond Math Soc 24(3):507–530, 1972) of homomorphic images of a bounded distributive lattice by means of closed subsets of its Priestley space. We also show how to modify the notions of generalized Priestley quasi-order and Vietoris family to obtain the dual characterizations of subalgebras and homomorphic images of bounded implicative semilattices, which generalize the well-known dual characterizations of subalgebras and homomorphic images of Heyting algebras (Esakia, Sov Math Dokl 15:147–151, 1974).
Ending Page	220
Page Count	20
Starting Page	201
File Format	PDF
ISSN	01678094
e-ISSN	15729273
Journal	Order
Issue Number	2
Volume Number	28
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-07-28
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Semilattices Geometry Implicative semilattices Convex and Discrete Geometry Structure and representation theory Distributive semilattices Duality theory Theory of Computation Heyting algebras
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Computational Theory and Mathematics Geometry and Topology

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