{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T04:26:13Z","timestamp":1761366373635,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T00:00:00Z","timestamp":1761177600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Nanjing Agricultural University College Students' Innovative Training Program","award":["X2025103070154"],"award-info":[{"award-number":["X2025103070154"]}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2019M651764"],"award-info":[{"award-number":["2019M651764"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11601231"],"award-info":[{"award-number":["11601231"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper introduces and investigates Ore extensions in the context of multiplier Hopf coquasigroups, a structure that generalizes both multiplier Hopf algebras and Hopf coquasigroups. We establish necessary and sufficient conditions under which an Ore extension of a regular multiplier Hopf coquasigroup itself forms a regular multiplier Hopf coquasigroup. Furthermore, we explore the isomorphism problem for such Ore extensions, providing criteria for the equivalence of two extensions. The case of multiplier Hopf coquasigroups is also analyzed, with conditions derived for the Ore extension to inherit the structure. Our results unify and extend prior work on Ore extensions in the settings of Hopf algebras, multiplier Hopf algebras, and Hopf coquasigroups.<\/jats:p>","DOI":"10.3390\/axioms14110778","type":"journal-article","created":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T02:34:45Z","timestamp":1761273285000},"page":"778","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Ore Extensions of Multiplier Hopf Coquasigroups"],"prefix":"10.3390","volume":"14","author":[{"given":"Rui","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Sciences, Nanjing Agricultural University, Nanjing 210095, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Na","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Sciences, Nanjing Agricultural University, Nanjing 210095, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yapeng","family":"Zeng","sequence":"additional","affiliation":[{"name":"College of Sciences, Nanjing Agricultural University, Nanjing 210095, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2084-5532","authenticated-orcid":false,"given":"Tao","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Sciences, Nanjing Agricultural University, Nanjing 210095, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"917","DOI":"10.2307\/2154659","article-title":"Multiplier Hopf algebras","volume":"342","author":"Daele","year":"1994","journal-title":"Trans. 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