{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T15:24:49Z","timestamp":1768663489584,"version":"3.49.0"},"reference-count":23,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T00:00:00Z","timestamp":1768521600000},"content-version":"vor","delay-in-days":15,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2026,1]]},"abstract":"<jats:p>In this paper, we investigate the structural properties of hyper ideals in hyper hoop\u2010algebras, a generalization of hoop\u2010algebras under the framework of hyperstructures. Building upon foundational concepts in hyper group theory and hoop theory, the study introduces definitions for hyper ideals and weak hyper ideals, as well as their absorptive and implicative variants. Various properties, examples, and characterizations of these ideals are presented. Additionally, the paper explores quotient structures and homomorphisms in the context of hyper hoop\u2010algebras, and establishes connections between different classes of ideals through a series of theorems. These results extend classical ideal theory and provide new insights into the algebraic structure and logic of hyper hoop\u2010algebras.<\/jats:p>","DOI":"10.1155\/jama\/3986328","type":"journal-article","created":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T06:59:06Z","timestamp":1768633146000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Some Properties of Hyper Ideals in Hyper Hoop\u2010Algebras"],"prefix":"10.1155","volume":"2026","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9832-9522","authenticated-orcid":false,"given":"Teferi Getachew","family":"Alemayehu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6673-9914","authenticated-orcid":false,"given":"Wondosen Zemene","family":"Norahun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1179-7057","authenticated-orcid":false,"given":"Derso Abeje","family":"Engidaw","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6735-6832","authenticated-orcid":false,"given":"Gezahagne Mulat","family":"Addis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Berhanu Bekele","family":"Belayneh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,1,16]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"crossref","first-page":"257","DOI":"10.4064\/fm-64-3-257-287","article-title":"Komplementare Halbgruppen Axiomatik und Aritmetik","volume":"64","author":"Bosbach B.","year":"1969","journal-title":"Fundamenta Mathematicae"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-69-1-1-14"},{"key":"e_1_2_9_3_2","volume-title":"Trends in Logic-Studia Logica Library 4","author":"H\u00e1jek P.","year":"1998"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.21136\/MB.2019.0140-17"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-023-08807-4"},{"key":"e_1_2_9_6_2","first-page":"45","volume-title":"Proceedings of the 8th Congress Mathematiciens Scan-Dinaves","author":"Marty F.","year":"1934"},{"key":"e_1_2_9_7_2","article-title":"Prolegomena of Hypergroup Theory","author":"Corsini P.","year":"1993","journal-title":"Aviani"},{"key":"e_1_2_9_8_2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3714-1","volume-title":"Applications of Hyper Structure Theory, Advances in Mathematics","author":"Corsini P.","year":"2003"},{"key":"e_1_2_9_9_2","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.fss.2016.12.012","article-title":"Hyper Effect Algebras","volume":"326","author":"Dvure\u010denskij A.","year":"2017","journal-title":"Fuzzy Sets and Systems"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200710082"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200910011"},{"key":"e_1_2_9_12_2","first-page":"493","article-title":"Strong Hyper BCK-Ideals of Hyper BCK-Algebras","volume":"51","author":"Jun Y. 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