Shahryari, MohammadLadra González, ManuelZargeh, Chia2018-08-172018-08-172018http://hdl.handle.net/10347/17252In this work we introduce the Higman-Neumann-Neumann (HNN)- extensions and the appropriate embedding theorems for dialgebras and Leibniz algebras. Due to the importance of the connection between the dialgebras and Leibniz algebras and the relationship between associative algebras and Lie algebras, we recall the theory of Groebner-Shirshov bases, and the Composition-Diamond Lemma in associative algebras and Lie algebras, as well as the theory of Groebner-Shirshov bases for dialgebras. As an application of the HNN-extensions of dialgebras and Leibniz algebras, we provide embedding theorems for dialgebras and Leibniz algebras, respectively: every dialgebra embeds inside its any HNN-extension and every Leibniz algebra embeds inside its any HNN-extension.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Álgebras de Leibniz y de LieDiálgebrasBases de Groebner-ShirshovExtensiones HNNTeoremas de encajeMaterias::Investigación::12 Matemáticas::1201 Algebra::120109 Algebra de LieMaterias::Investigación::12 Matemáticas::1201 Algebra::120112 Algebras no asociativasdoctoral thesisopen access