Year: 2025
Type: preprint
Abstract: For a hypergroup $(H,\circ)$ we consider $γ^{\ast}$, as the smallest equivalence relation on $H$ such that the quotion $(H/γ^{\ast},\tiny{\otimes})$ is an abelian group. We study some more properties of $γ^{\ast}$. Initially, it is investigated which subhypergroup the congruence relation modulo is strongly regular on, and its quotient results in an abelian group? This is directly related to the fundamental relation $γ^{\ast}$, since such subhypergroups must contain $S_γ$. Then, we examine the functor $γ^{\ast}$ from a categorical perspective and investigate properties such as continuity and cocontinuity concerning it using the decomposition $γ=δ\tiny{\ast}β$. For this purpose, we define the reduced words on strongly regular hypergroups. This has a direct application in studying how the functor $γ^{\ast}$ affects on the stalks of the sheaves of hypergroups.
Source: arXiv (Cornell University)
Authors: Afshar, Behnam, Ameri, Reza
Institution: University of Tehran
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415186147
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