*Result*: Computation in Algebraic Hyperstructures.
*Further Information*
*The concept of the relation β plays a central role in the study of hypercompositional structures. In this paper, we extend the definition of β to the general framework of hypergroupoids and develop an algorithm to compute its elements and its transitive closure β ★ . We then apply this algorithm to determine the β -class of partial identities in a hypergroup, a process equivalent to computing the heart of the given algebraic structure. Furthermore, we propose a more general algorithm that is also applicable to the case of H v -groups. By extracting the quotient set with respect to β ★ and endowing it with an appropriate group structure, we obtain the so-called fundamental group. The identity of this fundamental group can then be computed directly, yielding the heart of the structure. [ABSTRACT FROM AUTHOR]
Copyright of Computation is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)*