Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

For citation:

Bredikhin D. A., Popovich A. V. On Variety of Semigroups of Reletions with Operation of Reflexive Double Cylindrification. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, vol. 15, iss. 1, pp. 13-21. DOI: 10.18500/1816-9791-2015-15-1-13-22, EDN: TMMCIL

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
02.03.2015
Full text:
download
(downloads: 130)
Language: 
Russian
Heading: 
Mathematics
UDC: 
501.1
DOI: 
10.18500/1816-9791-2015-15-1-13-22
EDN: 
TMMCIL

On Variety of Semigroups of Reletions with Operation of Reflexive Double Cylindrification

Autors: 
Bredikhin Dmitry Aleksandrovich, Yuri Gagarin State Technical University of Saratov
Popovich A. V., Yuri Gagarin State Technical University of Saratov
Abstract: 

In the paper, the basis of identities for the variety generated by semigroups of relations with the operation of reflexive double cylindrification is found.

Key words: 
algebras of relations
varieties
basis of identities
operation of reflexive double cylindrification
References: 
  1. Tarski A. On the calculus of relations // J. Symbolic Logic. 1941. № 4. С. 73–89.
  2. Schein B. M. Relation algebras and function semigroups // Semigroup Forum. 1970. Vol. 1, № 1. P. 1–62.
  3. Бредихин Д. А. Об алгебрах отношений с диофантовыми операциями // Докл. АН. 1998. Т. 360. С. 594–595.
  4. Бредихин Д. А. О квазитождествах алгебр отношений с диофантовыми операциями // Сиб. матем. журн. 1997. № 38. C. 29–41.
  5. Böner P., Pöschel F. R. Clones of operations on binary relations // Contributions to general algebras. 1991. Vol. 7. P. 50–70.
  6. Henkin L., Monk J. D., Tarski A. Cylindric Algebras. Amsterdam, North-Holland, 1971.
  7. Kuhn S. The domino relations : flattening a twodimensional logic // J. Philosophical Logic. 1989. Vol. 18. P. 173–195.
  8. Venema Y. Many-dimansional modal logic. Amsterdam, Universiteit van Amsterdam, 1989.
  9. Jόnsson B. Varieties of relation algebras // Algebra Univers. 1982. Vol. 54. P. 273–299.
  10. Schein B. M. Representation of involuted semigroups by binary relations // Fundamenta Math. 1974. Vol. 82, № 2. P. 121–141.
  11. Bredikhin D. A. On varieties of semigroups of relations with operations of cylindrification // Contributions to General Algebra. 2005. Vol. 16. P. 1–6.
  12. Бредихин Д. А., Попович А. В. Тождества полугрупп отношений с операцией рефлексивной двойной цилиндрофикации // Изв. вузов. Матем. 2014. № 8. C. 90–95.
  13. Бредихин Д. А. Эквациональная теория алгебр отношений с позитивными операциями // Изв. вузов. Матем. 1993. № 3. C. 23–30.
Received: 
20.10.2014
Accepted: 
27.02.2015
Published: 
31.03.2015
  • 781 reads