Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

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Bredikhin D. A., Kvitka A. A., Tavaniuk M. R. On associative conjunctive operations on binary relations. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2026, vol. 26, iss. 3, pp. 323-334. DOI: 10.18500/1816-9791-2026-26-3-323-334, EDN: GRCPOV

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.08.2026
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Language: 
English
Heading: 
Mathematics
Article type: 
Article
UDC: 
501.1
DOI: 
10.18500/1816-9791-2026-26-3-323-334
EDN: 
GRCPOV

On associative conjunctive operations on binary relations

Autors: 
Bredikhin Dmitry Aleksandrovich, Saratov State University
Kvitka Alla Andreevna, Saratov State University
Tavaniuk Maksim R., Saratov State University
Abstract: 

A set of binary relations closed with respect to some collection of operations on them forms an algebra called an algebra of relations. Algebras of relations can be viewed as partially ordered by the set-theoretic inclusion. Theory of algebras of relations is an essential part of modern algebraic logic and has numerous applications in semigroup theory. As a rule, operations on relations are specified using logical formulas. An operation on relations is called conjunctive if it can be defined by a first-order formula containing only conjunctions. The paper is devoted to the study of associative binary conjunctive operations on relations, that is, classes of semigroups of relations with conjunctive operations. A classification of conjunctive operations is carried out, all associative operations are identified, and problems of finding axiomatic characteristics for most of them are solved.

Key words: 
algebra of relations
conjunctive operation
variety
quasi-variety
groupoid
semigroup
partially ordered semigroup
Acknowledgments: 
This work was supported by the Russian Science Foundation (project No. 25-21-00508).
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Received: 
24.03.2026
Accepted: 
23.04.2026
Published: 
31.08.2026
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