Generalized Digroups

Salazar-Díaz, Olga Patricia; Velásquez, Raúl; Wills-Toro, L. A.

doi:10.1080/00927872.2015.1065841

Cited by 14 publications

(21 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section we brie y recall some de nitions and results about generalized digroups, for a deeper study see [1]. We also review some properties and we introduce the notion of anti-homomorphism and involution for this structure.…”

Section: Some Results About Generalized Digroupsmentioning

confidence: 99%

“…For this generalized digroup we have that the halo is E = {x , x } Among many basic properties that are proved in [1], we state a couple of them that are being used later. It is easy to see that the halo also corresponds to any of the following sets…”

Section: De Nition 1 a Set D Is A Generalized Digroup If It Has Two mentioning

confidence: 99%

“…As it is shown in [1] a characterization of D is given below In addition, if ϕ is a bijection, then ϕ is a generalized isomorphism and D is isomorphic to D .…”

Section: De Nition 1 a Set D Is A Generalized Digroup If It Has Two mentioning

confidence: 99%

“…A slightly di erent structure studied in [1] is called generalized digroup. It doesn't request bilateral inverses for its elements.…”

Section: Introductionmentioning

confidence: 99%

“…The paper is organized as follows. In Section 2, we review the basic theory and the notions of subdigroup and normality in the sense of [1] and we introduce the de nitions of anti-homomorphisms and involutions over generalized digroups.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Augmented, free and tensor generalized digroups

2019

View full text Add to dashboard Cite

The concept of generalized digroup was proposed by Salazar-Díaz, Velásquez and Wills-Toro in their paper “Generalized digroups” as a non trivial extension of groups. In this way, many concepts and results given in the category of groups can be extended in a natural form to the category of generalized digroups. The aim of this paper is to present the construction of the free generalized digroup and study its properties. Although this construction is vastly different from the one given for the case of groups, we will use this concept, the classical construction for groups and the semidirect product to construct the tensor generalized digroup as well as the semidirect product of generalized digroups. Additionally, we give a new structural result for generalized digroups using compatible actions of groups and an equivariant map from a group set to the group corresponding to notions of associative dialgebras and augmented racks.

show abstract

Section: Some Results About Generalized Digroupsmentioning

confidence: 99%

Section: De Nition 1 a Set D Is A Generalized Digroup If It Has Two mentioning

confidence: 99%

“…As it is shown in [1] a characterization of D is given below In addition, if ϕ is a bijection, then ϕ is a generalized isomorphism and D is isomorphic to D .…”

Section: De Nition 1 a Set D Is A Generalized Digroup If It Has Two mentioning

confidence: 99%

“…A slightly di erent structure studied in [1] is called generalized digroup. It doesn't request bilateral inverses for its elements.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations