On semigroups of relations with the operation of the rectangular product
- Authors: Bredikhin D.A.1,2
-
Affiliations:
- Saratov State University
- Yuri Gagarin State Technical University of Saratov
- Issue: Vol 24, No 3 (2024)
- Pages: 320-329
- Section: Mathematics
- URL: https://journals.rcsi.science/1816-9791/article/view/353372
- DOI: https://doi.org/10.18500/1816-9791-2024-24-3-320-329
- EDN: https://elibrary.ru/DGQYFY
- ID: 353372
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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 theory of algebras of relations is an essential part of modern algebraic logic and has numerous applications in semigroup theory. The following problems naturally arise when classes of algebras of relation are considered: find a system of axioms for these classes, and find a basis of of identities (quasi-identities) for the varieties (quasi-varieties) generated by these classes. In the paper, these problems are solved for the class of semigroups of relation with the binary associative operation of the rectangular product, the result of which is the Cartesian product of the first projection of the first relation on the second projection of the second one.
About the authors
Dmitry Aleksandrovich Bredikhin
Saratov State University; Yuri Gagarin State Technical University of Saratov
ORCID iD: 0000-0003-3600-1294
SPIN-code: 2239-2268
Astrahanskaya str., 83, Saratov, Russia
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