Binary relations as lattice isomorphisms

Autor:	Darel W. Hardy, Mario Petrich
Rok vydání:	1999
Předmět:	Set (abstract data type) Combinatorics Transitive relation Binary relation Semigroup Applied Mathematics Lattice (order) Of the form Multiplication Isomorphism Mathematics
Zdroj:	Annali di Matematica Pura ed Applicata. 177:195-224
ISSN:	1618-1891 0373-3114
DOI:	10.1007/bf02505909
Popis:	In 1963, Zaretskiį established a one-to-one correspondence between the setBX of binary relations on a set X and the set of triples of the form (W, ϕ, V) where W and V are certain lattices and ϕ: W→V is an isomorphism. We provide a multiplication for these triples making the Zaretskiį correspondence a semigroup isomorphism. In addition, we consider faithful representations ofBX by pairs of partial transformations and also as the translational hull of its rectangular relations. Using these triples, we study idempotents, regular and completely regular elements and relationsH-equivalent to some relations with familiar properties such as reflexivity, transitivity, etc.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5da4515cf1bee18d0468abf037b07259 https://doi.org/10.1007/bf02505909 Zobrazit plný text záznamu Full text from SpringerLink