On semigroups of relations with the operation of the rectangular product

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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

References

  1. Schein B. M. Relation algebras and function semigroups. Semigroup Forum, 1970, vol. 1, iss. 4, pp. 1–62. https://doi.org/10.1007/BF02573019
  2. Tarski A. On the calculus of relations. The Journal of Symbolic Logic, 1941, vol. 6, iss. 3, pp. 73–89. https://doi.org/10.2307/2268577
  3. Tarski A. Contributions to the theory of models, III. Indagationes Mathematicae (Proceedings), 1955, vol. 58, pp. 56–64. https://doi.org/10.1016/S1385-7258(55)50009-6
  4. Lyndon R. C. The representation of relation algebras, II. Annals of Mathematics, 1956, vol. 63, iss. 2, pp. 294–307. https://doi.org/10.2307/1969611
  5. Monk D. On representable relation algebras. Michigan Mathematical Journal, 1964, vol. 11, iss. 3, pp. 207–210. https://doi.org/10.1307/mmj/1028999131
  6. Jonsson B. Representation of modular lattices and of relation algebras. Transactions of the American Mathematical Society, 1959, vol. 92, pp. 449–464. https://doi.org/10.1090/S0002-9947-1959-0108459-5
  7. Haiman M. Arguesian lattices which are not type-1. Algebra Universalis, 1991, vol. 28, pp. 128–137. https://doi.org/10.1007/BF01190416
  8. Andreka H., Bredikhin D. A. The equational theory of union-free algebras of relations. Algebra Universalis, 1995, vol. 33, pp. 516–532. https://doi.org/10.1007/BF01225472
  9. Boner P., Poschel F. R. Clones of operations on binary relations. Contributions to General Algebra, 1991, vol. 7, pp. 50–70.
  10. Bredikhin D. A. On quasi-identities of relation algebras with diophantine operations. Siberian Mathematical Journal, 1997, vol. 38, pp. 23–33. https://doi.org/10.1007/BF02674896
  11. Bredikhin D. A. On groupoids of relations with one conjunctive operation of rank 2. Studia Logica, 2022, vol. 110, pp. 1137–1153. https://doi.org/10.1007/s11225-022-09993-2
  12. Schein B. M. Semigroups of rectangular binary relations. Soviet Mathematics. Doklady, 1965, vol. 6, iss. 6, pp. 1563–1566.

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