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Binary representations of algebras with at most two binary operations. A Cayley theorem for distributive lattices. (English) Zbl 1174.06006

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.

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
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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
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