Movsisyan, Yu. M. Binary representations of algebras with at most two binary operations. A Cayley theorem for distributive lattices. (English) Zbl 1174.06006 Int. J. Algebra Comput. 19, No. 1, 97-106 (2009). The notion of binary representation of algebras with at most two binary operations is introduced in this paper, and the binary version of Cayley’s theorem for distributive lattices is given by hyperidentities. In particular, the author gets the binary version of Cayley’s theorem for De Morgan and Boolean algebras. Reviewer: Dimitru Buşneag (Craiova) Cited in 21 Documents MSC: 06D05 Structure and representation theory of distributive lattices 06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects) 06E05 Structure theory of Boolean algebras 08A62 Finitary algebras 20M30 Representation of semigroups; actions of semigroups on sets Keywords:binary representation; binary Cayley theorem; hyperidentity; semigroup; quasigroup; lattice; distributive lattice; De Morgan algebra; Boolean algebra PDFBibTeX XMLCite \textit{Yu. M. Movsisyan}, Int. J. Algebra Comput. 19, No. 1, 97--106 (2009; Zbl 1174.06006) Full Text: DOI References: [1] Movsisyan Yu. M., Izv. Akad. Nauk SSSR Ser. Mat. 53 pp 1040– [2] DOI: 10.4213/rm9 · doi:10.4213/rm9 [3] DOI: 10.2307/2324751 · Zbl 0749.08002 · doi:10.2307/2324751 [4] Chajda I., Demonstratio Math. pp 601– [5] DOI: 10.1142/S0218196701000681 · Zbl 1025.06007 · doi:10.1142/S0218196701000681 [6] DOI: 10.1142/S0218196798000156 · Zbl 0939.06009 · doi:10.1142/S0218196798000156 [7] Movsisyan Yu. M., Izv. Ross. Akad. Nauk, Ser. Mat. 56 pp 654– [8] DOI: 10.4213/im98 · doi:10.4213/im98 [9] Skornjakov L. A., Studia Sci. Math. Hungar. 16 pp 25– [10] DOI: 10.1007/BF02573602 · Zbl 0549.68049 · doi:10.1007/BF02573602 [11] DOI: 10.1142/4953 · doi:10.1142/4953 [12] Chajda I., Czech. Math. J. 43 pp 635– [13] DOI: 10.1090/S0002-9947-1957-0094404-6 · doi:10.1090/S0002-9947-1957-0094404-6 [14] Belousov V. D., Uspekhi Mat. Nauk. 20 pp 75– [15] Aczel J., Algebra Univers. 3 pp 1– [16] Movsisyan Yu. M., Introduction to the Theory of Algebras with Hyperidentities (1986) · Zbl 0675.08001 [17] Movsisyan Yu. M., Hyperidentities and Hypervarieties in Algebras (1990) [18] DOI: 10.1007/BF02188010 · Zbl 0491.08009 · doi:10.1007/BF02188010 [19] DOI: 10.1007/BF02188011 · Zbl 0453.08003 · doi:10.1007/BF02188011 [20] Denecke K., Hyperidentities and Clones (2000) · Zbl 0960.08001 [21] Koppitz J., M-Solid Varieties of Algebras (2006) · Zbl 1094.08001 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.