Geodesic
Existentially closed Leibniz algebras and an embedding theorem
Communications in Mathematics, Tome 29 (2021) no. 2, pp. 163-170

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MR Zbl
In this paper we introduce the notion of existentially closed Leibniz algebras. Then we use HNN-extensions of Leibniz algebras in order to prove an embedding theorem.
In this paper we introduce the notion of existentially closed Leibniz algebras. Then we use HNN-extensions of Leibniz algebras in order to prove an embedding theorem.
Classification : 16S15, 17A32, 17A36
Keywords: Existentially closed; Leibniz algebras; HNN-extension 
Zargeh, Chia. Existentially closed Leibniz algebras and an embedding theorem. Communications in Mathematics, Tome 29 (2021) no. 2, pp. 163-170. http://geodesic.mathdoc.fr/item/COMIM_2021_29_2_a0/
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[1] Bloh, A.: A generalization of the concept of a Lie algebra. Sov. Math. Dokl., 6, 1965, 1450-1452,

[2] Casas, J. M., Fernandez-Casado, R., García-Martínez, X., Khalmadze, E.: Actor of a crossed module of Leibniz algebras. Theory and Applications of Categories, 33, 2, 2018, 23-42,

[3] Higman, G., Neumann, B. H., Neumann, H.: Embedding theorems for groups. J. London. Math. Soc, 24, 1949, 247-254, | DOI

[4] Higman, G., Scotty, E. L.: Existentially closed groups. 1988, Clarendon Press,

[5] Kolesnikov, P. S., Makar-Limanov, L. G., Shestakov, I. P.: The Freiheitssatz for Generic Poisson Algebras. SIGMA, 10, 2014, 115-130,

[6] Ladra, M., Páez-Guillán, P., Zargeh, C.: HNN-extension of Lie superalgebras. Bull. Malays. Math. Sci. Soc., 43, 2020, 1959-1970, | DOI

[7] Ladra, M., Shahryari, M., Zargeh, C.: HNN-extensions of Leibniz algebras. Journal of Algebra, 532, 12, 2019, 183-200, | DOI

[8] J.,-L, Loday: Une Version non commutative des algebras de Lie: les algebras de Leibniz. Enseign. Math., 39, 1993, 269-293,

[9] Lyndon, R. C., Schupp, P. E.: Combinatorial Group Theory. 2001, Springer-Verlag, New York, | Zbl

[10] Scott, W. R.: Algebraically closed groups. Proc. of AMS, 1, 2, 1951, 118-121,

[11] Shahryari, M.: Existentially closed structures and some embedding theorems. Mathematical Notes, 101, 6, 2017, 1023-1032, | DOI

[12] Silvestrov, S., Zargeh, C.: HNN-extension of involutive multiplicative Hom-Lie algebras. arXiv:2101.01319 [math.RA], 2021, preprint.