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A latticial study of complete hypergroups
1  University of Life Sciences, Iasi, Romania
Academic Editor: Miriam Cohen

https://doi.org/10.3390/Symmetry2021-10755 (registering DOI)
Abstract:

The dihedral group represents a group of symmetries of a regular polygon. Moreover, it is generated by rotation and axial symmetries. Due to this structure, in a recently published paper, we analyzed the HX-groups associated with them and we computed the commutativity degree of the associated HX-groups. Since there is an interesting connection between the HX-groups and the complete hypergroups- both of them can be constructed using the structure of a group, in this paper, we aim to determine the relationships between the lattice of the dihedral group and the lattice of the associated HX-groups, as well as that of the associated complete hypergroups. Furthermore, we will present some conditions to describe the modular and the distributive lattices, using elements from hypercompositional algebra. This has the advantage that the interaction called hyperproduct or hyperoperation between two elements of the considered set is not anymore just an element, as in the classical algebra, but a subset of the support set.

Keywords: Dihedral group, lattice, HX-groups, complete hypergroup
Comments on this paper
Florin Nichita
Hi, we would like to collaborate on these topics.
We would like to collaborate on these topics:

Nichita, F.; Oner, T.; KALKAN, T.; Senturk, I.; Terziler, M. Perspectives on the Yang-Baxter Equation in Bck-Algebras. Preprints 2021, 2021020425 (doi: 10.20944/preprints202102.0425.v1). Nichita, F.; Oner, T.; KALKAN, T.; Senturk, I.; Terziler, M. Perspectives on the Yang-Baxter Equation in Bck-Algebras. Preprints 2021, 2021020425 (doi: 10.20944/preprints202102.0425.v1).Copy
Sonea Andromeda
Dear Professor Nichita,

Thank you very much for your proposal. I would like to collaborate, but first of all I have to study these BCK algebras, because I don't know very much about them.

Best wishes,

Andromeda Sonea



 
 
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