{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T03:42:12Z","timestamp":1776397332482,"version":"3.51.2"},"reference-count":18,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T00:00:00Z","timestamp":1767052800000},"content-version":"vor","delay-in-days":363,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"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":[[2025,1]]},"abstract":"<jats:p>\n                    It is known that the class of hoops is ideally determined, in the sense that every filter of any hoop  is a 1\u2010class of a unique congruence relation on . This confirms that every filter in a hoop determines one and only one quotient structure. So, given a hoop  and a filter\n                    <jats:italic>\u03c0<\/jats:italic>\n                    of , it is natural to question ourselves what should be the defining properties of\n                    <jats:italic>\u03c0<\/jats:italic>\n                    so that the quotient  is a join hoop (respectively, a Wajsberg hoop, cancellative hoop, and an MV\u2010algebra) and what should be the property of\n                    <jats:italic>\u03c0<\/jats:italic>\n                    such that  is a subdirectly irreducible. In this paper, we answer these questions by introducing some new types of filters in hoops called\n                    <jats:italic>J<\/jats:italic>\n                    \u2010filters,\n                    <jats:italic>w<\/jats:italic>\n                    \u2010filters, MV\u2010filters,\n                    <jats:italic>c<\/jats:italic>\n                    \u2010filters, and completely prime filters, respectively.\n                  <\/jats:p>","DOI":"10.1155\/jama\/1357590","type":"journal-article","created":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T16:50:38Z","timestamp":1767113438000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Studying the Theory of Hoops Through Some Type of Filters"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6735-6832","authenticated-orcid":false,"given":"Gezahagne Mulat","family":"Addis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Terefe Getachew","family":"Beyene","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,12,30]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-64-3-257-287"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-69-1-1-14"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-007-9078-1"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-152553"},{"key":"e_1_2_10_5_2","volume-title":"Mathematics of Fuzzy Logic, Trends in Logic-Studia Logica Library 4","author":"H\u00e1jek P.","year":"1998"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01195727"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.5373\/jarpm.1895.120113"},{"key":"e_1_2_10_8_2","first-page":"619","article-title":"Filter Theory of Pseudo Hoop-Algebras","volume":"37","author":"Alavi S. Z.","year":"2017","journal-title":"Italian Journal of Pure and Applied Mathematics"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-007-0178-7"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s000120050156"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200910025"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1080\/27684830.2024.2378544"},{"key":"e_1_2_10_13_2","first-page":"48","article-title":"Ideals in BCK-Algebras Which Are Lower Semilattices","volume":"10","author":"Palasinski M.","year":"1981","journal-title":"Bulletin of the Section of Logic"},{"key":"e_1_2_10_14_2","first-page":"5","article-title":"Wajsberg Algebras","volume":"8","author":"Font J. M.","year":"1984","journal-title":"Stochastica"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1958-0094302-9"},{"key":"e_1_2_10_16_2","first-page":"153","article-title":"Pseudo-Hoops","volume":"11","author":"Georgescu G.","year":"2005","journal-title":"Journal of Multiple-Valued Logic and Soft Computing"},{"key":"e_1_2_10_17_2","volume-title":"Partially Ordered Algebraic Systems","author":"Fuchs L.","year":"1963"},{"key":"e_1_2_10_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8130-3"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/1357590","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/jama\/1357590","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/1357590","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T02:44:55Z","timestamp":1776393895000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/jama\/1357590"}},"subtitle":[],"editor":[{"given":"AbdelMaksoud","family":"Soliman","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/jama\/1357590"],"URL":"https:\/\/doi.org\/10.1155\/jama\/1357590","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"2025-01-15","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-09-26","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-12-30","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"1357590"}}