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@article{ADM_2018_25_2_a6, author = {Yuri Movsisyan}, title = {On functional equations and distributive second order formulae with specialized quantifiers}, journal = {Algebra and discrete mathematics}, pages = {269--285}, publisher = {mathdoc}, volume = {25}, number = {2}, year = {2018}, language = {en}, url = {http://geodesic.mathdoc.fr/item/ADM_2018_25_2_a6/} }
TY - JOUR AU - Yuri Movsisyan TI - On functional equations and distributive second order formulae with specialized quantifiers JO - Algebra and discrete mathematics PY - 2018 SP - 269 EP - 285 VL - 25 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ADM_2018_25_2_a6/ LA - en ID - ADM_2018_25_2_a6 ER -
Yuri Movsisyan. On functional equations and distributive second order formulae with specialized quantifiers. Algebra and discrete mathematics, Tome 25 (2018) no. 2, pp. 269-285. http://geodesic.mathdoc.fr/item/ADM_2018_25_2_a6/
[1] J. Aczel, Vorlesungen über Functionalgleichungen und ihre Anwendungem, VEB Deutsch. Verl. Wiss, Berlin, 1961 | MR
[2] J. Aczel, “Quelque problèmes non-résolus dans la théorie des équations fonctionelles”, Neki Nerešeni Problemi u Matematici, Beograd, 1963, 149–152 | Zbl
[3] J. Aczel, J. Dhombres, Functional equations in several variables with applications to mathematics, information theory and to the natural and social sciences, Cambridge University Press, Cambridge, 1991 | MR
[4] M. Aguiar, M. Livernet, “The associative operad and the weak order on the symmetric groups”, J. Homotopy Relat. Struct., 2 (2007), 57–84 | MR | Zbl
[5] A. A. Albert, “Quasigroup I”, Trans. Amer. Math. Soc., 54 (1943), 507–519 | DOI | MR | Zbl
[6] A. A. Albert, “Quasigroup II”, Trans. Amer. Math. Soc., 55 (1944), 401–419 | DOI | MR | Zbl
[7] A. D. Anosov, “On homomorphisms of many-sorted algebraic systems in connection with cryptographic applications”, Discrete Math. Appl., 17:4 (2007), 331–347 | DOI | MR | Zbl
[8] W. E. Barnes, “On $\Gamma$-rings of Nobusawa”, Pacific J. Math., 3 (1966), 411–422 | DOI | MR
[9] V. D. Belousov, “The structure of distributive quasigroups”, Mat. Sb. (N.S.), 50(92):3 (1960), 267–298 | MR | Zbl
[10] V. D. Belousov, “Systems of quasigroups with generalized identities”, Russian Math. Surveys, 20 (1965), 73–143 | DOI | MR
[11] V. D. Belousov, Foundations of the theory of quasigroups and loops, Nauka, Moscow, 1967 (Russian) | MR
[12] V. D. Belousov, Yu. M. Movsisyan, “On the rank of generalized identities”, Izv. Akad. Nauk. Arm., Ser. Mat., 9 (1974), 135–142 | MR | Zbl
[13] G. M. Bergman, An invitation on general algebra and universal constructions, ed. Second edition, Springer, 2015 | MR
[14] G. M. Bergman, “Hyperidentities of groups and semigroups”, Aequationes Math., 23 (1981), 50–65 | DOI | MR | Zbl
[15] S. L. Bloom, Z. Esik, E. G. Manes, “A Cayley theorem for Boolean algebras”, Amer. Math. Monthly, 97 (1990), 831–833 | DOI | MR | Zbl
[16] R. H. Bruck, A survey of binary systems, Springer-Verlag, 1971 | MR
[17] S. Burris, H. P. Sankappanavar, A course in universal algebra, Springer-Verlag, 1981 | MR | Zbl
[18] A. Church, Introduction to mathematical logic, v. I, Princeton University Press, Princeton, NJ, 1956 | MR | Zbl
[19] K. Denecke, S. L. Wismath, Hyperidentities and Clones, Gordon and Breach Science Publishers, 2000 | MR | Zbl
[20] J. Denes, A. D. Keedwell, Latin squares and their applications, Akademiai Kiado, Budapest; Academic Press, New York; English Universities Press, London, 1974 | MR | Zbl
[21] P. S. Gevorgyan, “On binary $G$-spaces”, Math. Notes, 96:4 (2014), 600–602 | DOI | MR
[22] E. Graczynska, Algebras of $M$-solid quasivarieties, Siatras International Bookshop, Athens, 2014
[23] G. Grätzer, Universal Algebra, ed. 2nd edition, Springer-Verlag, New York, 1979 | Zbl
[24] A. Knoebel, A. Romanowska, Distributive Multisemilattices, Dissertationes Mathematicae (Rozprawy Marhematyczne), Warszawa, 1991 | MR | Zbl
[25] J. Koppitz, K. Denecke, $M$-Solid Varieties of Algebras, Springer, 2006 | MR | Zbl
[26] A. Krapez̆, “Functional equations of generalized associativity, bisymmetry, transitivity and distributivity”, Publ. Inst. Math. (Beograd), 30 (1981), 81–87 | MR | Zbl
[27] A. Krapez̆, “Generalized associativity on groupoids”, Publ. Inst. Math. (Beograd), 28 (1980), 105–112 | MR | Zbl
[28] A. Krapez̆, “Cryptographically Suitable Quasigroups via Functional Equations”, ICT Innovations 2012, AISC, 207, eds. S. Markovski and M. Gusev, Springer-Verlag, Berlin–Heidelberg, 2013, 265–274
[29] A. Krapez̆, “Quadratic level quasigroup equations with four variables. I”, Publ. Inst. Math. (Beograd) (N.S.), 81(95) (2007), 53–67 | DOI | MR | Zbl
[30] A. Krapez̆, “Quadratic level quasigroup equations with four variables. II”, Publ. Inst. Math. (Beograd) (N.S.), 93(107) (2013), 29–47 | DOI | MR | Zbl
[31] A. G. Kurosh, Lectures on general algebra, Chelsea, New York, 1963 | MR
[32] J.-L. Loday, M. O. Ronco, “Order structure on the algebra of permutations and of planar binary trees”, J. Algebraic Combin., 15 (2002), 253–270 | DOI | MR | Zbl
[33] A. I. Mal'tsev, “Model correspondences”, Izv. Akad. Nauk SSSR, Ser. Mat., 23:3 (1959), 313–336 | MR | Zbl
[34] A. I. Mal'cev, “Some problems in the theory of classes of models”, Proceedings of IV All-Union Mathematical Congress (Leningrad), Publishing House of the USSR Academy of Sciences, Leningrad, 1963, 169–198
[35] A. I. Mal'cev, Algebraic systems, Grundlehren der mathematischen Wissenschaften, 192, Springer, New-York, 1973
[36] H. B. Mann, “The construction of ortogonal Lattin squares”, Ann. Math. Statist., 13 (1942), 418–423 | DOI | MR | Zbl
[37] H. B. Marandjian, “On computable solutions to functional equations”, CSIT, 2011, 20–22
[38] H. B. Marandjian, Selected Topics in Recursive Function Theory in Computer Science, DTH, Lyngby, 1990
[39] H. B. Marandjian, “General Form Recursive Equations I”, Computer Science Logic, Selected Papers, Lecture Notes in Computer Science, 933, Springer, Berlin–Heidelberg, 1995 | MR | Zbl
[40] S. V. Matveev, “Distributive groupoids in knot theory”, Mat. Sb. (N.S.), 119:1 (1982), 78–88 | MR
[41] R. Moufang, “Zur Structur von Alternativkörpern”, Math. Ann., 110 (1935), 416–430 | DOI | MR
[42] Yu. M. Movsisyan, “Biprimitive classes of algebras of second degree”, Mat. Issled. Akad. Nauk. Mold., 9 (1974), 70–82 | MR | Zbl
[43] Yu. M. Movsisyan, Introduction to the theory of algebras with hyperidentities, Yerevan State University Press, 1986 (Russian) | MR
[44] Yu. M. Movsisyan, “The multiplicative group of field and hyperidentities”, Math. USSR Izvestiya, 35 (1990), 337–391 | DOI | MR
[45] Yu. M. Movsisyan, Hyperidentities and hypervarieties in algebras, Yerevan State University Press, 1990 (Russian) | MR
[46] Yu. M. Movsisyan, “Hyperidentities in algebras and varieties”, Russian Math. Surveys, 53 (1998), 57–108 | DOI | MR | Zbl
[47] Yu. M. Movsisyan, “Hyperidentities and hypervarieties”, Sci. Math. Jpn., 54:3 (2001), 595–640 | MR | Zbl
[48] Yu. M. Movsisyan, “Binary representations of algebras with at most two binary operations. A Cayley theorem for distributive lattices”, International Journal of Algebra and Computation, 19:1 (2009), 97–106 | DOI | MR | Zbl
[49] Yu. M. Movsisyan, “Hyperidentities and related concepts, I”, Arm. J. Math., 2 (2017), 146–222 | MR | Zbl
[50] Yu. M. Movsisyan, “Hyperidentities and related concepts, II”, Arm. J. Math., 1 (2018), 1–90 | MR
[51] Yu. M. Movsisyan, E. Nazari, “A Cayley theorem for the multiplicative semigroup of a field”, Journal of Algebra and Its Applications, 11:2 (2012), 1–12 | MR
[52] Yu. M. Movsisyan, E. Nazari, “Transitive Modes”, Demonstratio Math., 44:3 (2011), 511–522 | MR | Zbl
[53] N. Nobusawa, “On a generalization of the ring theory”, Osaka J. Math., 1 (1964), 81–89 | MR | Zbl
[54] R. Padmanabhan, P. Penner, “Lattice ordered polynomial algebras”, Order, 15 (1998), 75–86 | DOI | MR | Zbl
[55] V. Pambuccian, “Euclidean geometry problems rephrased in terms of midpoints and point-reflections”, Elem. Math., 60 (2005), 19–24 | DOI | MR | Zbl
[56] T. Pirashvili, “Sets with two associative operations”, Cent. Eur. J. Math., 2 (2003), 169–183 | DOI | MR | Zbl
[57] H. Pflugfelder, Quasigroups and Loops, Introduction, Heldermann Verlag, Berlin, 1990 | MR | Zbl
[58] B. I. Plotkin, Universal algebra, algebraic logic, and databases, Kluwer Academic Publisher, 1994 | MR | Zbl
[59] J. H. Przytycki, “Knot and distributive homology: from arc colorings to Yang-Baxter homology”, New Ideas in Low Dimensional Topology, 2015, 413–488 | DOI | MR | Zbl
[60] B. Richter, Dialgebren, Doppelalgebren und ihre Homologie, Diplomarbeit, Universitat Bonn, 1997 https://www.math.uni-hamburg.de/home/richter/publications.html | Zbl
[61] Romanowska A., Smith J. D. H., Modes, World Scientific, 2002 | MR | Zbl
[62] M. K. Sen, “On $\Gamma$-semigroup”, Algebra and Its Applications (New Delhi, 1981), Lecture Notes in Pure and Appl. Math., 91, Dekker, New York, 1984, 301–308 | MR
[63] M. K. Sen, N. K. Saha, “On $\Gamma$-semigroup I”, Bull. Calcutta Math. Soc., 78 (1986), 180–186 | MR | Zbl
[64] A. Seth, “$\Gamma$-group congruences on regular $\Gamma$-semigroups”, Int. J. Math. Math. Sci., 15:1 (1992), 103–106 | DOI | MR | Zbl
[65] J. Slominski, “On the satisfiabilities and varieties for abstract algebras induced by the cones and functor dynamics”, Demonstratio Math., 26:1 (1993), 11–22 | MR | Zbl
[66] J. D. H. Smith, An Introduction to Quasigroups and Their Representations, Chapman Hall/Crc, 2006 | MR
[67] J. D. H. Smith, “On groups of hypersubstitutions”, Algebra Universalis, 64 (2010), 39–48 | DOI | MR | Zbl
[68] J. D. H. Smith, A. B. Romanowska, Post-Modern Algerbra, Wiley, New York, 1999 | MR
[69] S. K. Stein, “On the foundation of quasigroups”, Trans. Amer. Math. Soc., 85 (1957), 228–256 | DOI | MR | Zbl
[70] W. Taylor, “Hyperidentities and hypervarieties”, Aequationes Math., 23 (1981), 30–49 | DOI | MR | Zbl
[71] K. Urbanik, “On algebraic operations in idempotent algebras”, Colloquium Math., 13 (1965), 129–157 | DOI | MR | Zbl
[72] K. A. Zaretskii, “Abstract characteristics of bisemigroups of binary operations”, Math. Notes, 1:5 (1967), 347–350 | DOI | MR
[73] A. V. Zhuchok, “Free products of doppelsemigroups”, Algebra Universalis, 77 (2017), 361–374 | DOI | MR | Zbl
[74] A. V. Zhuchok, M. Demko, “Free $n$-dinilpotent doppelsemigroups”, Algebra Discrete Math., 22 (2016), 304–316 | MR | Zbl
[75] A. V. Zhuchok, “Dimonoids and bar-units”, Sib. Math. J., 56:5 (2015), 827–840 | DOI | MR | Zbl
[76] A. V. Zhuchok, “Structure of relatively free dimonoids”, Commun. Algebra, 45:4 (2017), 1639–1656 | DOI | MR | Zbl