{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T03:13:54Z","timestamp":1772853234017,"version":"3.50.1"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"20","license":[{"start":{"date-parts":[[2021,8,21]],"date-time":"2021-08-21T00:00:00Z","timestamp":1629504000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,21]],"date-time":"2021-08-21T00:00:00Z","timestamp":1629504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s00500-021-06071-y","type":"journal-article","created":{"date-parts":[[2021,8,21]],"date-time":"2021-08-21T01:03:40Z","timestamp":1629507820000},"page":"12703-12715","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Preideals in EQ-algebras"],"prefix":"10.1007","volume":"25","author":[{"given":"N.","family":"Akhlaghinia","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7538-7885","authenticated-orcid":false,"given":"R. A.","family":"Borzooei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. Aaly","family":"Kologani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,8,21]]},"reference":[{"issue":"2","key":"6071_CR1","doi-asserted-by":"publisher","first-page":"141","DOI":"10.21136\/MB.2019.0140-17","volume":"145","author":"M Aaly Kologani","year":"2020","unstructured":"Aaly Kologani M, Borzooei RA (2020) On ideal theory of hoops. Mathematica Bohemica 145(2):141\u2013162","journal-title":"Mathematica Bohemica"},{"key":"6071_CR2","doi-asserted-by":"crossref","unstructured":"Akhlaghinia N, Aaly Kologani M, Borzooei RA, Xin XL (2021) The category of EQ-algebras. Bull Sect Logic. https:\/\/doi.org\/10.18778\/0138-0680.2021.01","DOI":"10.18778\/0138-0680.2021.01"},{"key":"6071_CR3","doi-asserted-by":"crossref","unstructured":"Borzooei RA, Ganji B (2015) States on EQ-algebras. J Intell Fuzzy Syst 29:209\u2013221","DOI":"10.3233\/IFS-151588"},{"key":"6071_CR4","doi-asserted-by":"crossref","unstructured":"Burris S, Sankappanavar HP (1981) A course in universal algebra (Graduate Texts in Mathematics), Springer-Verlag, 78","DOI":"10.1007\/978-1-4613-8130-3"},{"key":"6071_CR5","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/s00500-012-0915-4","volume":"17","author":"I Chajda","year":"2013","unstructured":"Chajda I, K\u00fchr J (2013) Ideals and congruences of basic algebras. Soft Comput 17:401\u2013410","journal-title":"Soft Comput"},{"key":"6071_CR6","doi-asserted-by":"crossref","unstructured":"Cignoli R, D\u2019ottaaviano I, Mundici D (2000) Algebraic foundations of many valued reasoning, Kluwer Academic Publishers, Dordrecht, Boston-London","DOI":"10.1007\/978-94-015-9480-6"},{"key":"6071_CR7","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/j.fss.2014.11.019","volume":"292","author":"M Dyba","year":"2016","unstructured":"Dyba M, El-Zekey M, Nov\u00e1k V (2016) Non-commutative first-order $$EQ$$-logics. Fuzzy Sets and Syst 292:215\u2013241","journal-title":"Fuzzy Sets and Syst"},{"issue":"9","key":"6071_CR8","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.1007\/s00500-009-0491-4","volume":"14","author":"M El-Zekey","year":"2010","unstructured":"El-Zekey M (2010) Representable good $$EQ$$-algebras. Soft Comput 14(9):1011\u20131023","journal-title":"Soft Comput"},{"key":"6071_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.fss.2011.05.011","volume":"178","author":"M El-Zekey","year":"2011","unstructured":"El-Zekey M, Nov\u00e1k V, Mesiar R (2011) On good $$EQ$$-algebras. Fuzzy Sets and Syst 178:1\u201323","journal-title":"Fuzzy Sets and Syst"},{"issue":"3","key":"6071_CR10","first-page":"443","volume":"54","author":"LC Holdon","year":"2018","unstructured":"Holdon LC (2018) On ideals in Demorgan residuated lattices. Kybernetika 54(3):443\u2013475","journal-title":"Kybernetika"},{"key":"6071_CR11","doi-asserted-by":"publisher","first-page":"1201","DOI":"10.1007\/s11225-012-9457-0","volume":"100","author":"S Jenei","year":"2012","unstructured":"Jenei S (2012) Equality algebras. Studia Logica 100:1201\u20131209","journal-title":"Studia Logica"},{"key":"6071_CR12","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/j.fss.2012.09.014","volume":"218","author":"C Lele","year":"2013","unstructured":"Lele C, Nganou JB (2013) $$MV$$- algebras derived from ideals in BL-algebras. Fuzzy Sets and Syst 218:103\u2013113","journal-title":"Fuzzy Sets and Syst"},{"key":"6071_CR13","doi-asserted-by":"publisher","first-page":"2087","DOI":"10.3233\/IFS-130884","volume":"26","author":"LZ Liu","year":"2014","unstructured":"Liu LZ, Zhang XY (2014) Implicative and positive implicative prefilters of $$EQ$$-algebras. J Intell Fuzzy Syst 26:2087\u20132097","journal-title":"J Intell Fuzzy Syst"},{"key":"6071_CR14","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/j.fss.2016.04.015","volume":"311","author":"N Mohtashamnia","year":"2017","unstructured":"Mohtashamnia N, Torkzadeh L (2017) The lattice of prefilters of an $$EQ$$-algebra. Fuzzy Sets and Syst 311:86\u201398","journal-title":"Fuzzy Sets and Syst"},{"key":"6071_CR15","unstructured":"Nov\u00e1k V (2006) $$EQ$$- algebras: Primary concepts and properties, in: Proc. Czech-Japan Seminar, Ninth Meeting, Kitakyushu and Nagasaki, Graduate School of Information, Waseda University, August 18-22"},{"key":"6071_CR16","doi-asserted-by":"publisher","first-page":"512","DOI":"10.1093\/jigpal\/jzp087","volume":"19","author":"V Nov\u00e1k","year":"2011","unstructured":"Nov\u00e1k V (2011) $$EQ$$- algebras-based fuzzy type theory and its extensions. Logic J IGPL 19:512\u2013542","journal-title":"Logic J IGPL"},{"issue":"7","key":"6071_CR17","doi-asserted-by":"publisher","first-page":"2956","DOI":"10.1016\/j.fss.2009.04.010","volume":"160","author":"V Nov\u00e1k","year":"2009","unstructured":"Nov\u00e1k V, De Baets B (2009) $$EQ$$- algebras. Fuzzy Sets and Syst 160(7):2956\u20132978","journal-title":"Fuzzy Sets and Syst"},{"key":"6071_CR18","doi-asserted-by":"publisher","first-page":"2113","DOI":"10.2298\/FIL1907113P","volume":"33","author":"A Paad","year":"2019","unstructured":"Paad A (2019) Ideals in bounded equality algebras. Filomat 33:2113\u20132123","journal-title":"Filomat"},{"issue":"3","key":"6071_CR19","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1515\/ms-2017-0369","volume":"70","author":"XL Xin","year":"2020","unstructured":"Xin XL, Ma YC, Fu YL (2020) The existence of states on $$EQ$$-algebras. Mathematica Slovaca 70(3):527\u2013546","journal-title":"Mathematica Slovaca"},{"key":"6071_CR20","doi-asserted-by":"publisher","first-page":"7495","DOI":"10.1007\/s00500-018-03687-5","volume":"23","author":"J Yang","year":"2019","unstructured":"Yang J, Zhang X (2019) Finite direct product of $$EQ$$algebras. Soft Comput 23:7495\u20137504","journal-title":"Soft Comput"},{"key":"6071_CR21","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/j.ins.2016.11.027","volume":"381","author":"F Zebardast","year":"2017","unstructured":"Zebardast F, Borzooei RA, Aaly Kologhani M (2017) Results on equality algebras. Inform Sci 381:270\u2013282","journal-title":"Inform Sci"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-021-06071-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-021-06071-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-021-06071-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,23]],"date-time":"2021-09-23T10:07:58Z","timestamp":1632391678000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-021-06071-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,21]]},"references-count":21,"journal-issue":{"issue":"20","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["6071"],"URL":"https:\/\/doi.org\/10.1007\/s00500-021-06071-y","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-462251\/v1","asserted-by":"object"}]},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,21]]},"assertion":[{"value":"22 July 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 August 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that there is no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Human and animal rights"}}]}}