Cayley-type theorems for $g$-dimonoids
DOI:
https://doi.org/10.52737/18291163-2020.12.3-1-14Keywords:
$g$-dimonoid, dimonoid, act of set, dialgebra, morphism of acts, $(l, r)$-morphism of semigroupAbstract
In this paper we prove Cayley-type theorems for $g$-dimonoids using the left (right) acts of sets and concept of dialgebra.
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References
J.L. Loday, Dialgebras. Dialgebras and Related Operads, Lect. Notes Math., Springer, Berlin, (2001), pp. 7-66. https://doi.org/10.1007/3-540-45328-8_2
Yu. M. Movsisyan, S. Davidov and M. Safaryan, Construction of free g-dimonoids, Algebra Discrete Math., 18 (2014), no. 1, pp. 138-148.
A. V. Zhuchok and A. B. Gorbatkov, On the structure of dimonoids, Semigroup Forum, (2016), pp. 194-203. https://doi.org/10.1007/s00233-016-9795-8
A. Church, Introduction to Mathematical Logic Vol.1, Princeton University Press, Princeton, 1956.
A.I. Mal'tsev, Some questions of the theory of classes of models (in Russian), Proceedings of the IV-th All-Union Mathematical Congress, 1, (1963), pp. 169-198.
A.I. Mal'tsev, Algebraic systems, Springer-Verlag, Berlin-Heidelberg-New York, 1973.
Yu. M. Movsisyan, Introduction to the theory of algebras with hyperidentities (in Russian), Yerevan State University Press, 1986.
Yu. M. Movsisyan, Hyperidentities and hypervarieties in algebras (in Russian), Yerevan State University Press, 1990.
Yu. M. Movsisyan, Hyperidentities in algebras and varieties, Uspekhi Mat. Nauk, 53 (1), (1998), pp. 61-114, Russian Math. Surveys, 53 (1), (1998), pp. 57-108. https://doi.org/10.1070/rm1998v053n01abeh000009
Yu. M. Movsisyan, Hyperidentities and Related Concepts. I, Armen. J. Math., 2, (2017), pp. 146-222.
Yu. M. Movsisyan, Hyperidentities and Related Concepts. II, Armen. J. Math., 4, (2018), pp. 1-85.
L. A. Skornyakov (Editor), General algebra. V. 2 (in Russian), Moscow, 1991.
Yu. M. Movsisyan, Hyperidentities and hypervarieties, Scientiae Mathematicae Japonicae, 54 (2001), no. 3, pp. 595-640.
Yu. M. Movsisyan, Biprimitive classes of algebras of second degree (in Russian), Matematicheskie Issledovaniya, 9 (1974), pp. 70-84.
W.~E. Barnes, On Γ-rings of Nobusawa, Pacific J. Math., 3 (1966), pp. 411-422.
N. Kehayopulu, On regular duo po-Γ-semigroups, Math. Slovaca, 61 (2011), no. 6, pp. 871-884. https://doi.org/10.2478/s12175-011-0054-x
J. Luh, On the theory of simple Γ-rings, Michigan Math. J., 16 (1969), pp. 65-75.
N. Nobusawa, On a generalization of the ring theory, Osaka J. Math., 1 (1964), pp. 81-89.
S. K. Sardar, S. Gupta and K. P. Shum, Γ-semigroups with unities and Morita equivalence for monoids, European Journal of Pure and Applied Mathematics, 6 (2013), no. 1, pp. 1-10.
M.K. Sen, On Γ-semigroup, In: Algebra and Its Applications, New Delhi (1981), Lecture Notes in Pure and Appl. Math., Dekker, New York, 91 (1984), pp. 301-308.
M.K. Sen and N.K. Saha, On Γ-semigroup-I, Bull. Calcutta Math. Soc., 78 (1986), pp. 180-186.
A. Seth, $Gamma$-group congruences on regular Γ-semigroups, Int. J. Math. Math. Sci., 15 (1992), no. 1, pp. 103-106.
M.K. Sen and S. Chattopadhyay, Γ-Semigroups. A Survey, In Book: Algebra and Its Applications, 2016.
A.V. Zuchok, Relatively free doppelsemigroups, Potsdam University Press, 2018.
A.V. Zuchok, Y.V. Zhuchok and J. Koppitz, Free rectangular doppelsemigroups, J. Algebra Appl., September (2019). https://doi.org/10.1142/s0219498820502059
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