Skip to main content
Log in

On Varieties of Groupoids of Relations with Operation of Binary Cylindrification

  • Published:
Algebra universalis Aims and scope Submit manuscript

Abstract

In this paper, bases of identities of varieties generated by classes of partially ordered groupoids of relations with the operation of binary cylindrification are found.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Andréka H., Bredikhin D.A.: The equational theory of union-free algebras of relations. Algebra Universalis 33, 516–532 (1994)

    Article  Google Scholar 

  2. Andréka H., Mikulás Sz.: Axiomatizability of positive algebras of binary relations. Algebra Universalis. 66, 7–34 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  3. Andréka, H., Neméti, I., Sain, I.: Algebraic Logic. In: Handbook of Philosophical Logic, vol 2, 2nd ed., pp. 133–247. Kluwer Academic Publishers (2001)

  4. Bredikhin, D.A. On relation algebras with general superpositions. In: Andréka, H., Monk, J., Németi I. (eds.) Algebraic Logic, vol. 54, pp. 111–124. North-Holland, Amsterdam (1991)

  5. Bredikhin D.A.: Varieties of groupoids associated with involuted restrictive bisemigroups of binary relations. Semigroup Forum 44, 87–192 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bredikhin D.A.: The equational theory of algebras of relations with positive operations. Izv. Vyssh. Uchebn. Zaved. Mat. 3, 23–30 (1993)

  7. Bredikhin D.A.: On quasi-identities of algebras of relations with Diophantine operations. Sib. Math. J. 38, 23–33 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bredikhin D.A.: Reducts of Tarski relation algebras. Algebra and Logic 37, 1–8 (1998)

    Article  MathSciNet  Google Scholar 

  9. Bredikhin D.A.: On algebras of relations with Diophantine operations. Dokl. Math. 57, 435–436 (1998)

    Google Scholar 

  10. Bredikhin, D.A.: On varieties of groupoids of binary relations. Izv. Sarat. Univ. N.S. Ser. Math. Mech. Inform. 13, iss. 1, pt. 1, 13–21 (2013) (Russian)

  11. Bredikhin, D.A.: On varieties of groupoids of relations with Diophantine operations. Izv. Sarat. Univ. N.S. Ser. Math. Mech. Inform. 13, iss. 4, pt. 2, 28–34 (2013) (Russian)

  12. Böner P., Pöschel F.R.: Clones of operations on binary relations. Contributions to general algebra 7, 50–70 (1991)

    Google Scholar 

  13. Cupona, G., Celakoski, N., Janeva, B.: Variety of groupoids with axioms of the form x m+1 yxy and/or xy n+1xy. Glas. Mat. Ser. III 37(57), 235–244 (2002)

  14. Dudek J.: Varieties of idempotent commutative groupoids. Fund. Math. 120, 193–204 (1984)

    MATH  MathSciNet  Google Scholar 

  15. Gratzer G., Padmanabhan R.: On idempotent commutative nonassociative groupoids. Proc. Amer. Math. Soc. 28, 75–80 (1971)

    Article  MathSciNet  Google Scholar 

  16. Henkin L., Monk J. D., Tarski A.: Cylindric Algebras Part I. North Holland, Amsterdam (1971)

    Google Scholar 

  17. Jezek J., Kepka T.: The lattice of varieties of commutative abelian distributive groupoids. Algebra Universalis 5, 225–237 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  18. Jónsson B.(1982) Varieties of relation algebras. Algebra Universalis 15, 273–298

  19. McKenzie R., Freese R., Jezek J., Jipsen P., Markovic P., Maroti M.: The variety generated by order algebras. Algebra Universalis 47, 103–138 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  20. Monk J.D: On representable relation algebras. Michigan Math. J. 11, 207–210 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  21. Phillips J. D.: Short equational bases for two varieties of groupoids associated with involuted restrictive bisemigroups of binary relations. Semigroup Forum 73, 308–312 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  22. Schein B.M.: Relation algebras and function semigroups. Semigroup Forum 1, 1–62 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  23. Schein, B.M.: Representation of subreducts of Tarski relation algebras. In: Andréka, H., Monk, J., Németi I. (eds.) Algebraic Logic, vol. 54, pp. 621–635. North-Holland, Amsterdam (1991)

  24. Tarski A.: On the calculus of relations. J. Symbolic Logic 6, 73–89 (1941)

    Article  MathSciNet  Google Scholar 

  25. Tarski, A., Givant, S. R.: A formalization of set theory without variables. Amer. Math. Soc. Colloquium Publications, vol. 41, Providence

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dmitry A. Bredikhin.

Additional information

Presented by I. Hodkinson.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bredikhin, D.A. On Varieties of Groupoids of Relations with Operation of Binary Cylindrification. Algebra Univers. 73, 43–52 (2015). https://doi.org/10.1007/s00012-014-0313-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00012-014-0313-0

2010 Mathematics Subject Classification

Key words and phrases

Navigation