Dudek, Wiesław A.; Trokhimenko, Valentin S. Projection representable relations on Menger \((2,n)\)-semigroups. (English) Zbl 1165.20324 Czech. Math. J. 58, No. 4, 1015-1037 (2008). Summary: Abstract characterizations of relations of nonempty intersection, inclusion and 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. Cited in 2 Documents MSC: 20N15 \(n\)-ary systems \((n\ge 3)\) 08A62 Finitary algebras Keywords:\(n\)-place functions; algebras of functions; Menger algebras; \((2,n)\)-semigroups PDFBibTeX XMLCite \textit{W. A. Dudek} and \textit{V. S. Trokhimenko}, Czech. Math. J. 58, No. 4, 1015--1037 (2008; Zbl 1165.20324) Full Text: DOI arXiv EuDML References: [1] W. A. Dudek and V. S. Trokhimenko: Functional Menger \( \mathcal{P} \) -algebras. Commun. Algebra 30 (2002), 5921–5931. · Zbl 1018.20057 · doi:10.1081/AGB-120016022 [2] W. A. Dudek and V. S. Trokhimenko: Representations of Menger (2, n)-semigroups by multiplace functions. Commun. Algebra 34 (2006), 259–274. · Zbl 1092.20051 · doi:10.1080/00927870500346255 [3] 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.) · Zbl 1115.08001 [4] H. B. Mann: On orthogonal Latin squares. Bull. Amer. Math. Soc. 50 (1944), 249–257. · Zbl 0060.32307 · doi:10.1090/S0002-9904-1944-08127-5 [5] V. Novák and M. Novotný: Transitive ternary relations and quasiorderings. Arch. Math. (Brno) 1/2 (1989), 5–12. · Zbl 0714.06001 [6] J. Riguet: Relations binaires, fermetures, correspondances de Galois. Bull. Soc. Math. France 76 (1948), 114–155. · Zbl 0033.00603 [7] 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.) [8] B. M. Schein: Projection partitions of function semigroups. Math. Rep. Acad. Sci., R. Soc. Canada 1 (1979), 67–70. [9] B. M. Schein: Lectures on semigroups of transformations. Amer. Math. Soc. Translat. 113 (1979), 123–181. · Zbl 0404.20057 [10] B. M. Schein and V. S. Trohimenko: Algebras of multiplace functions. Semigroup Forum 17 (1979), 1–64. · Zbl 0397.08001 · doi:10.1007/BF02194309 [11] F. N. Sokhatskij: An abstract characterization of (2, n)-semigroups of n-ary operations. Mat. Issled. 65 (1982), 132–139. (In Russian.) [12] V. S. Trokhimenko: Ordered algebras of multiplace functions. Izv. Vyssh. Uchebn. Zaved. Matematika 1 (1971), 90–98. (In Russian.) · Zbl 0221.08001 [13] V. S. Trokhimenko: Abstract characterizations of some algebras of multiplace functions. Izv. Yyssh. Uchebn. Zaved. Matematika 4 (1971), 87–95. (In Russian.) · Zbl 0221.08002 [14] 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.) [15] V. S. Trokhimenko: Stationary subsets and stabilizers of restrictive Menger P-algebras of multiplace functions. Algebra Universalis 44 (2000), 129–142. · Zbl 1014.08004 · doi:10.1007/s000120050175 [16] T. Yakubov: On (2, n)-semigroups of n-ary operations. Bull. Akad. Ştiinţa SSR Moldov. 1 (1974), 29–46. (In Russian.) · Zbl 0308.20049 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.