{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T15:23:48Z","timestamp":1772119428486,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T00:00:00Z","timestamp":1649116800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T00:00:00Z","timestamp":1649116800000},"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":[[2022,6]]},"DOI":"10.1007\/s00500-022-06972-6","type":"journal-article","created":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T07:09:31Z","timestamp":1649142571000},"page":"5057-5067","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Derivations of equality algebras"],"prefix":"10.1007","volume":"26","author":[{"given":"Gholam Reza","family":"Rezaei","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mona Aaly","family":"Kologani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rajab Ali","family":"Borzooei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Mohseni","family":"Takallo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,4,5]]},"reference":[{"issue":"2","key":"6972_CR1","first-page":"331","volume":"47","author":"M Aaly Kologani","year":"2020","unstructured":"Aaly Kologani M, Borzooei RA, Rezaei GR, Jun YB (2020) Commutative equality algebras and & -equality algebras. Annal Univ Craiova Math Com Sci Ser 47(2):331\u2013345","journal-title":"Annal Univ Craiova Math Com Sci Ser"},{"issue":"5","key":"6972_CR2","doi-asserted-by":"crossref","first-page":"815","DOI":"10.46793\/KgJMat2205.815K","volume":"45","author":"M Aaly Kologani","year":"2022","unstructured":"Aaly Kologani M, Mohseni Takallo M, Borzooei RA, Jun YB (2022) Right and left mappings in equality algebras. Kragujevac J Math 45(5):815\u2013832","journal-title":"Kragujevac J Math"},{"issue":"1&2","key":"6972_CR3","first-page":"13","volume":"46","author":"HAS Abujabal","year":"2006","unstructured":"Abujabal HAS, Al-shehri NO (2006) Some results on derivations of BCI-algebras. J Nat Sci Math 46(1&2):13\u201319","journal-title":"J Nat Sci Math"},{"issue":"3","key":"6972_CR4","first-page":"435","volume":"33","author":"HAS Abujabal","year":"2007","unstructured":"Abujabal HAS, Al-shehri NO (2007) On left derivations of BCI-algebras. Soochow J Math 33(3):435\u2013444","journal-title":"Soochow J Math"},{"issue":"1\u20132","key":"6972_CR5","first-page":"27","volume":"32","author":"AM Al-roqi","year":"2014","unstructured":"Al-roqi AM (2014) On generalized $$(\\alpha ,\\beta )$$-derivations in BCI-algebras. J Appl Math Inf 32(1\u20132):27\u201338","journal-title":"J Appl Math Inf"},{"issue":"32","key":"6972_CR6","first-page":"1491","volume":"6","author":"NO Al-shehri","year":"2012","unstructured":"Al-shehri NO, Bawazeer SM (2012) On derivations of BCC-algebras. Inter. J. Alg. 6(32):1491\u20131498","journal-title":"Inter. J. Alg."},{"key":"6972_CR7","doi-asserted-by":"crossref","unstructured":"Ardekani LK, Davvaz B (2014) On generalized derivations of BCI-algebras and their properties. J Math 2014, Article ID 207161, 10 pages","DOI":"10.1155\/2014\/207161"},{"key":"6972_CR8","doi-asserted-by":"crossref","unstructured":"Bawazeer SM, Alshehri NO, Babusail RS (2013) Generalized derivations of BCC-algebras. Int J Math Math Sci 2013, Article ID 451212, 4 pages","DOI":"10.1155\/2013\/451212"},{"key":"6972_CR9","doi-asserted-by":"publisher","first-page":"95","DOI":"10.7151\/dmgaa.1193","volume":"33","author":"RA Borzooei","year":"2013","unstructured":"Borzooei RA, Borumand Saeid A, Rezaei A, Radfar A, Ameri R (2013) On pseudo-BE algebras. Discuss Math Gen Algorithm Appl 33:95\u2013108","journal-title":"Discuss Math Gen Algorithm Appl"},{"key":"6972_CR10","first-page":"33","volume":"7","author":"RA Borzooei","year":"2017","unstructured":"Borzooei RA, Zebardast F, Aaly Kologani M (2017) Some types of filters in equality algebras. Categ Gen Algorithm Struct Appl 7:33\u201355","journal-title":"Categ Gen Algorithm Struct Appl"},{"key":"6972_CR11","doi-asserted-by":"publisher","first-page":"7505","DOI":"10.1007\/s00500-018-3032-1","volume":"22","author":"RA Borzooei","year":"2018","unstructured":"Borzooei RA, Zarean M, Zahiri O (2018) Involutive equality algebras. Soft Comput 22:7505\u20137517","journal-title":"Soft Comput"},{"issue":"6","key":"6972_CR12","first-page":"175","volume":"17","author":"LC Ciungu","year":"2020","unstructured":"Ciungu LC, Borumand Saeid A, Rezaei A (2020) Modal operators on pseudo-BE algebras. IJFS 17(6):175\u2013191","journal-title":"IJFS"},{"issue":"3","key":"6972_CR13","doi-asserted-by":"publisher","first-page":"321","DOI":"10.4134\/CKMS.2009.24.3.321","volume":"24","author":"MA Javed","year":"2009","unstructured":"Javed MA, Aslam M (2009) A note on $$f$$-derivations of BCI-algebras. Com Korea Math Soc 24(3):321\u2013331","journal-title":"Com Korea Math Soc"},{"key":"6972_CR14","doi-asserted-by":"crossref","unstructured":"Jenei S (2010) Equality algebras. In: Proceedings of CINTI 2010. Conference-11th IEEE international symposium on computational intelligence and informatics, Budapest, Hungary,","DOI":"10.1109\/CINTI.2010.5672249"},{"key":"6972_CR15","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. Stud Log 100:1201\u20131209","journal-title":"Stud Log"},{"key":"6972_CR16","doi-asserted-by":"crossref","unstructured":"Jenei S, K\u00f3r\u00f3di L (2011) On the variety of equality algebras. Fuzzy Log Tech 153\u2013155","DOI":"10.2991\/eusflat.2011.1"},{"key":"6972_CR17","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/j.ins.2003.03.001","volume":"159","author":"YB Jun","year":"2004","unstructured":"Jun YB, Xin XL (2004) On derivations of BCI-algebras. Inf Sci 159:167\u2013176","journal-title":"Inf Sci"},{"issue":"84","key":"6972_CR18","first-page":"4185","volume":"7","author":"KJ Lee","year":"2013","unstructured":"Lee KJ (2013) A new kind of derivation in BCI-algebras. Appl Math Sci 7(84):4185\u20134194","journal-title":"Appl Math Sci"},{"key":"6972_CR19","first-page":"107","volume":"9","author":"PH Lee","year":"1981","unstructured":"Lee PH, Lee TK (1981) On derivations of prime rings. Chin J Math 9:107\u2013110","journal-title":"Chin J Math"},{"issue":"2","key":"6972_CR20","first-page":"87","volume":"1","author":"SM Lee","year":"2012","unstructured":"Lee SM, Kim KH (2012) A note on $$f$$-derivations of BCC-algebras. Pure Math Sci 1(2):87\u201393","journal-title":"Pure Math Sci"},{"key":"6972_CR21","doi-asserted-by":"crossref","unstructured":"Muhiuddin G, Al-roqi AM (2012a) On $$(\\alpha ,\\beta )$$-derivations in BCI-algebras. Discrete Dyn Nat Soc 2012, Article ID 403209, 11 pages","DOI":"10.1155\/2012\/403209"},{"key":"6972_CR22","doi-asserted-by":"crossref","unstructured":"Muhiuddin G, Al-roqi AM (2012b) On $$t$$-derivations of BCI-algebras. Abstract Appl Anal 2012, Article ID 872784, 12 pages","DOI":"10.1155\/2012\/872784"},{"issue":"3","key":"6972_CR23","doi-asserted-by":"publisher","first-page":"1153","DOI":"10.12785\/amis\/080326","volume":"8","author":"G Muhiuddin","year":"2014","unstructured":"Muhiuddin G, Al-roqi AM (2014) On generalized left derivations in BCI-algebras. Appl Math Inf Sci 8(3):1153\u20131158","journal-title":"Appl Math Inf Sci"},{"key":"6972_CR24","doi-asserted-by":"crossref","unstructured":"Muhiuddin G, Al-roqi AM, Jun YB, Ceven Y (2013) On symmetric left bi-derivations in BCI-algebras. Int J Math Math Sci 2013, Article ID 238490, 6 pages","DOI":"10.1155\/2013\/238490"},{"issue":"1","key":"6972_CR25","first-page":"69","volume":"25","author":"F Nisar","year":"2009","unstructured":"Nisar F (2009a) Characterization of $$f$$-derivations of a BCI-algebra. East Asian Math J 25(1):69\u201387","journal-title":"East Asian Math J"},{"key":"6972_CR26","first-page":"176","volume":"5","author":"F Nisar","year":"2009","unstructured":"Nisar F (2009b) On $$F$$-derivations of BCI-algebras. J Prime Res Math 5:176\u2013191","journal-title":"J Prime Res Math"},{"issue":"20","key":"6972_CR27","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 Set Syst 160(20):2956\u20132978","journal-title":"Fuzzy Set Syst"},{"key":"6972_CR28","doi-asserted-by":"publisher","first-page":"1093","DOI":"10.1090\/S0002-9939-1957-0095863-0","volume":"8","author":"E Posner","year":"1957","unstructured":"Posner E (1957) Derivations in prime rings. Proc Am Math Soc 8:1093\u20131100","journal-title":"Proc Am Math Soc"},{"key":"6972_CR29","first-page":"398","volume":"43","author":"C Prabpayak","year":"2009","unstructured":"Prabpayak C, Leerawat U (2009) On derivation of BCC-algebras. Kasetsart J Nat Sci 43:398\u2013401","journal-title":"Kasetsart J Nat Sci"},{"issue":"1","key":"6972_CR30","first-page":"54","volume":"5","author":"C Prabpayak","year":"2009","unstructured":"Prabpayak C, Leerawat U (2009) On ideals and congruences in KU-algebras. Magna Sci 5(1):54\u201357","journal-title":"Magna Sci"},{"issue":"3","key":"6972_CR31","doi-asserted-by":"publisher","first-page":"345","DOI":"10.11568\/kjm.2016.24.3.345","volume":"24","author":"K Sawika","year":"2016","unstructured":"Sawika K, Intasan R, Kaewwasri A, Iampan A (2016) Derivations of UP-algebras. Korea J Math 24(3):345\u2013367","journal-title":"Korea J Math"},{"key":"6972_CR32","first-page":"307","volume":"25","author":"M Zarean","year":"2017","unstructured":"Zarean M, Borzooei RA, Zahiri O (2017) On state equality algebras. Quasi Rel Syst 25:307\u2013326","journal-title":"Quasi Rel Syst"},{"key":"6972_CR33","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 Kologani M (2017) Results on equality algebras. Inf Sci 381:270\u2013282","journal-title":"Inf Sci"},{"key":"6972_CR34","doi-asserted-by":"publisher","first-page":"1675","DOI":"10.1155\/IJMMS.2005.1675","volume":"2005","author":"J Zhan","year":"2005","unstructured":"Zhan J, Liu YL (2005) On $$f$$-derivations of BCI-algebras. Int J Math Math Sci 2005:1675\u20131684","journal-title":"Int J Math Math Sci"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-06972-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-022-06972-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-06972-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,31]],"date-time":"2023-01-31T11:51:39Z","timestamp":1675165899000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-022-06972-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,5]]},"references-count":34,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["6972"],"URL":"https:\/\/doi.org\/10.1007\/s00500-022-06972-6","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-1224210\/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":[[2022,4,5]]},"assertion":[{"value":"20 January 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 April 2022","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"}},{"value":"Informed consent was obtained from all individual participants included in the study.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}}]}}