Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Bredikhin D. A. On Semigroups of Relations with the Operation of Left and Right Rectangular Products. Izv. Sarat. Univ. Math. Mech. Inform., 2020, vol. 20, iss. 3, pp. 280-289. DOI: 10.18500/1816-9791-2020-20-3-280-289

Published online: 
31.08.2020
Full text:
(downloads: 250)
Language: 
English
Heading: 
Article type: 
Article
UDC: 
501.1
DOI: 
10.18500/1816-9791-2020-20-3-280-289

On Semigroups of Relations with the Operation of Left and Right Rectangular Products

Autors: 
Bredikhin Dmitry Aleksandrovich, Saratov State Technical University
Abstract: 

A set of binary relations closed with respect to some collection of operations on relations forms an algebra called an algebra of relations. The class of all algebras (partially ordered algebras) isomorphic to algebras (partially ordered by set-theoretic inclusion ⊆ algebras) of relations with operations from   is denoted by R{Ω} (R{Ω, ⊆}). An operation on relations is called primitive-positive if it can be defined by a formula of the first-order predicate calculus containing only existential quantifiers and conjunctions in its prenex normal form. We consider algebras of relations with associative primitive-positive operations ∗ and ⋆, defined by the following formulas ρ ∗ σ = {(u, v) : (∃ s, t, w) (u, s) ∈ ρ ∧ (t, w) ∈ σ} and ρ ⋆ σ = {(u, v) : (∃ s, t, w) (s, t) ∈ ρ ∧ (w, v) ∈ σ} respectively. The axiom systems for the classes R{∗}, R{∗, ⊆}, R{⋆}, R{⋆, ⊆}, and bases of quasi-identities and identities for quasi-varieties and varieties generated by these classes are found.

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Received: 
11.06.2019