{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T16:17:57Z","timestamp":1774973877343,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T00:00:00Z","timestamp":1762214400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Chongqing Science and Technology Commission","award":["CSTB2024NSCQ-LZX0083"],"award-info":[{"award-number":["CSTB2024NSCQ-LZX0083"]}]},{"name":"Natural Science Foundation of Chongqing Science and Technology Commission","award":["2023TIADZXX0017"],"award-info":[{"award-number":["2023TIADZXX0017"]}]},{"name":"Natural Science Foundation of Chongqing Science and Technology Commission","award":["CSTB2023NSCQ-LZX0135"],"award-info":[{"award-number":["CSTB2023NSCQ-LZX0135"]}]},{"name":"Scientific and Technological Research Program of Chongqing Municipal Education Commission","award":["KJZD-K202301023"],"award-info":[{"award-number":["KJZD-K202301023"]}]},{"name":"Scientific and Technological Research Program of Chongqing Municipal Education Commission","award":["KJQN202201209"],"award-info":[{"award-number":["KJQN202201209"]}]},{"name":"Scientific and Technological Research Program of Chongqing Municipal Education Commission","award":["233356"],"award-info":[{"award-number":["233356"]}]},{"name":"Scientific and Technological Research Program of Wanzhou District","award":["WZSTC-20230309"],"award-info":[{"award-number":["WZSTC-20230309"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12201086"],"award-info":[{"award-number":["12201086"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The concept of the relation \u03b2 plays a central role in the study of hypercompositional structures. In this paper, we extend the definition of \u03b2 to the general framework of hypergroupoids and develop an algorithm to compute its elements and its transitive closure \u03b2\u2605. We then apply this algorithm to determine the \u03b2-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 Hv-groups. By extracting the quotient set with respect to \u03b2\u2605 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.<\/jats:p>","DOI":"10.3390\/computation13110261","type":"journal-article","created":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T14:02:09Z","timestamp":1762264929000},"page":"261","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Computation in Algebraic Hyperstructures"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0465-3925","authenticated-orcid":false,"given":"Yuming","family":"Feng","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, Chongqing Three Gorges University, Chongqing 404100, China"}]},{"given":"Enrico","family":"Talotti","sequence":"additional","affiliation":[{"name":"Center for Information Technologies and Applied Mathematics, University of Nova Gorica, Vipavska 13, SI-5000 Nova Gorica, Slovenia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0177-4123","authenticated-orcid":false,"given":"Violeta","family":"Leoreanu-Fotea","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, \u201cAl.I. Cuza\u201d University, Bd. Carol I, No. 11, 700506 Ia\u015fi, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,4]]},"reference":[{"key":"ref_1","unstructured":"Marty, F. (1934, January 14\u201318). Sur une g\u00e9n\u00e9ralisation de la notion de groupe. Proceedings of the 8 \u00e8me Congr\u00e8s des Math\u00e9maticiens, Scandinaves, Stockholm, Sweden."},{"key":"ref_2","first-page":"525","article-title":"Remarques sur les hypergroupes","volume":"224","author":"Krasner","year":"1947","journal-title":"C. R. Acad. Sci."},{"key":"ref_3","unstructured":"Krasner, M. (1937). Sur la Primitivit\u00e9 des Corps B-Adiques, Mathematica."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"77","DOI":"10.2307\/2371563","article-title":"Hypergroups","volume":"59","author":"Wall","year":"1937","journal-title":"Amer. J. 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[8th ed.]."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/11\/261\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T05:31:10Z","timestamp":1762407070000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/11\/261"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,4]]},"references-count":35,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["computation13110261"],"URL":"https:\/\/doi.org\/10.3390\/computation13110261","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,4]]}}}