Abstract
Abstract characterizations of relations of nonempty intersection, inclusion end equality of domains for partial n-place functions are presented. Representations of Menger (2, n)-semigroups by partial n-place functions closed with respect to these relations are investigated.
Similar content being viewed by others
References
W. A. Dudek and V. S. Trokhimenko: Functional Menger \( \mathcal{P} \)-algebras. Commun. Algebra 30 (2002), 5921–5931.
W. A. Dudek and V. S. Trokhimenko: Representations of Menger (2, n)-semigroups by multiplace functions. Commun. Algebra 34 (2006), 259–274.
W. A. Dudek and V. S. Trokhimenko: Menger algebras of multiplace functions. Centrul Ed. USM. Khishinev, 2006, ISBN 978-9975-70-621-6. (In Russian.)
H. B. Mann: On orthogonal Latin squares. Bull. Amer. Math. Soc. 50 (1944), 249–257.
V. Novák and M. Novotný: Transitive ternary relations and quasiorderings. Arch. Math. (Brno) 1/2 (1989), 5–12.
J. Riguet: Relations binaires, fermetures, correspondances de Galois. Bull. Soc. Math. France 76 (1948), 114–155.
B. M. Schein: A relation of co-definability on semigroups of functions. Ordered sets and lattices 1 (1971), 86–89 (Izdat. Saratov. Gos. Univ.). (In Russian.)
B. M. Schein: Projection partitions of function semigroups. Math. Rep. Acad. Sci., R. Soc. Canada 1 (1979), 67–70.
B. M. Schein: Lectures on semigroups of transformations. Amer. Math. Soc. Translat. 113 (1979), 123–181.
B. M. Schein and V. S. Trohimenko: Algebras of multiplace functions. Semigroup Forum 17 (1979), 1–64.
F. N. Sokhatskij: An abstract characterization of (2, n)-semigroups of n-ary operations. Mat. Issled. 65 (1982), 132–139. (In Russian.)
V. S. Trokhimenko: Ordered algebras of multiplace functions. Izv. Vyssh. Uchebn. Zaved. Matematika 1 (1971), 90–98. (In Russian.)
V. S. Trokhimenko: Abstract characterizations of some algebras of multiplace functions. Izv. Yyssh. Uchebn. Zaved. Matematika 4 (1971), 87–95. (In Russian.)
V. S. Trokhimenko: Characterization of the co-definability relation on ordered algebras of multiplace functions. Izv. Vyssh. Uchebn. Zaved. Matematika 9 (1977), 80–88. (In Russian.)
V. S. Trokhimenko: Stationary subsets and stabilizers of restrictive Menger P-algebras of multiplace functions. Algebra Universalis 44 (2000), 129–142.
T. Yakubov: On (2, n)-semigroups of n-ary operations. Bull. Akad. Ştiinţa SSR Moldov. 1 (1974), 29–46. (In Russian.)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dudek, W.A., Trokhimenko, V.S. Projection representable relations on Menger (2, n)-semigroups. Czech Math J 58, 1015–1037 (2008). https://doi.org/10.1007/s10587-008-0065-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10587-008-0065-0