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.
Similar content being viewed by others
References
Andréka H., Bredikhin D.A.: The equational theory of union-free algebras of relations. Algebra Universalis 33, 516–532 (1994)
Andréka H., Mikulás Sz.: Axiomatizability of positive algebras of binary relations. Algebra Universalis. 66, 7–34 (2011)
Andréka, H., Neméti, I., Sain, I.: Algebraic Logic. In: Handbook of Philosophical Logic, vol 2, 2nd ed., pp. 133–247. Kluwer Academic Publishers (2001)
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)
Bredikhin D.A.: Varieties of groupoids associated with involuted restrictive bisemigroups of binary relations. Semigroup Forum 44, 87–192 (1992)
Bredikhin D.A.: The equational theory of algebras of relations with positive operations. Izv. Vyssh. Uchebn. Zaved. Mat. 3, 23–30 (1993)
Bredikhin D.A.: On quasi-identities of algebras of relations with Diophantine operations. Sib. Math. J. 38, 23–33 (1997)
Bredikhin D.A.: Reducts of Tarski relation algebras. Algebra and Logic 37, 1–8 (1998)
Bredikhin D.A.: On algebras of relations with Diophantine operations. Dokl. Math. 57, 435–436 (1998)
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)
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)
Böner P., Pöschel F.R.: Clones of operations on binary relations. Contributions to general algebra 7, 50–70 (1991)
Cupona, G., Celakoski, N., Janeva, B.: Variety of groupoids with axioms of the form x m+1 y = xy and/or xy n+1 = xy. Glas. Mat. Ser. III 37(57), 235–244 (2002)
Dudek J.: Varieties of idempotent commutative groupoids. Fund. Math. 120, 193–204 (1984)
Gratzer G., Padmanabhan R.: On idempotent commutative nonassociative groupoids. Proc. Amer. Math. Soc. 28, 75–80 (1971)
Henkin L., Monk J. D., Tarski A.: Cylindric Algebras Part I. North Holland, Amsterdam (1971)
Jezek J., Kepka T.: The lattice of varieties of commutative abelian distributive groupoids. Algebra Universalis 5, 225–237 (1975)
Jónsson B.(1982) Varieties of relation algebras. Algebra Universalis 15, 273–298
McKenzie R., Freese R., Jezek J., Jipsen P., Markovic P., Maroti M.: The variety generated by order algebras. Algebra Universalis 47, 103–138 (2002)
Monk J.D: On representable relation algebras. Michigan Math. J. 11, 207–210 (1964)
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)
Schein B.M.: Relation algebras and function semigroups. Semigroup Forum 1, 1–62 (1970)
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)
Tarski A.: On the calculus of relations. J. Symbolic Logic 6, 73–89 (1941)
Tarski, A., Givant, S. R.: A formalization of set theory without variables. Amer. Math. Soc. Colloquium Publications, vol. 41, Providence
Author information
Authors and Affiliations
Corresponding author
Additional information
Presented by I. Hodkinson.
Rights and permissions
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00012-014-0313-0