Existentially closed Leibniz algebras and an embedding theorem

Chia Zargeh

Communications in Mathematics (2021)

  • Volume: 29, Issue: 2, page 163-170
  • ISSN: 1804-1388

Abstract

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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.

How to cite

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Zargeh, Chia. "Existentially closed Leibniz algebras and an embedding theorem." Communications in Mathematics 29.2 (2021): 163-170. <http://eudml.org/doc/297500>.

@article{Zargeh2021,
abstract = {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.},
author = {Zargeh, Chia},
journal = {Communications in Mathematics},
keywords = {Existentially closed; Leibniz algebras; HNN-extension},
language = {eng},
number = {2},
pages = {163-170},
publisher = {University of Ostrava},
title = {Existentially closed Leibniz algebras and an embedding theorem},
url = {http://eudml.org/doc/297500},
volume = {29},
year = {2021},
}

TY - JOUR
AU - Zargeh, Chia
TI - Existentially closed Leibniz algebras and an embedding theorem
JO - Communications in Mathematics
PY - 2021
PB - University of Ostrava
VL - 29
IS - 2
SP - 163
EP - 170
AB - 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.
LA - eng
KW - Existentially closed; Leibniz algebras; HNN-extension
UR - http://eudml.org/doc/297500
ER -

References

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  3. Higman, G., Neumann, B. H., Neumann, H., 10.1112/jlms/s1-24.4.247, J. London. Math. Soc, 24, 1949, 247-254, (1949) DOI10.1112/jlms/s1-24.4.247
  4. Higman, G., Scotty, E. L., Existentially closed groups, 1988, Clarendon Press, (1988) 
  5. Kolesnikov, P. S., Makar-Limanov, L. G., Shestakov, I. P., The Freiheitssatz for Generic Poisson Algebras, SIGMA, 10, 2014, 115-130, (2014) 
  6. Ladra, M., Páez-Guillán, P., Zargeh, C., 10.1007/s40840-019-00783-z, Bull. Malays. Math. Sci. Soc., 43, 2020, 1959-1970, (2020) DOI10.1007/s40840-019-00783-z
  7. Ladra, M., Shahryari, M., Zargeh, C., 10.1016/j.jalgebra.2019.05.014, Journal of Algebra, 532, 12, 2019, 183-200, (2019) DOI10.1016/j.jalgebra.2019.05.014
  8. J.,-L, Loday, Une Version non commutative des algebras de Lie: les algebras de Leibniz, Enseign. Math., 39, 1993, 269-293, (1993) 
  9. Lyndon, R. C., Schupp, P. E., Combinatorial Group Theory, 2001, Springer-Verlag, New York, (2001) Zbl0997.20037
  10. Scott, W. R., Algebraically closed groups, Proc. of AMS, 1, 2, 1951, 118-121, (1951) 
  11. Shahryari, M., 10.1134/S0001434617050297, Mathematical Notes, 101, 6, 2017, 1023-1032, (2017) DOI10.1134/S0001434617050297
  12. Silvestrov, S., Zargeh, C., HNN-extension of involutive multiplicative Hom-Lie algebras, arXiv:2101.01319 [math.RA], 2021, preprint. (2021) 

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