{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:18:10Z","timestamp":1740107890974,"version":"3.37.3"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"21","license":[{"start":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T00:00:00Z","timestamp":1660608000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T00:00:00Z","timestamp":1660608000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Foundation of Chongqing Municipal Key Laboratory of Institutions of Higher Education","award":["[2017]3"],"award-info":[{"award-number":["[2017]3"]}]},{"name":"Foundation of Chongqing Development and Reform Commission","award":["2017[1007]"],"award-info":[{"award-number":["2017[1007]"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2022,11]]},"DOI":"10.1007\/s00500-022-07372-6","type":"journal-article","created":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T14:05:04Z","timestamp":1660658704000},"page":"11277-11286","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Skew polynomial superrings"],"prefix":"10.1007","volume":"26","author":[{"given":"Surdive","family":"Atamewoue Tsafack","sequence":"first","affiliation":[]},{"given":"Shiping","family":"Wen","sequence":"additional","affiliation":[]},{"given":"Babatunde Oluwaseun","family":"Onasanya","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0465-3925","authenticated-orcid":false,"given":"Yuming","family":"Feng","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,16]]},"reference":[{"key":"7372_CR1","first-page":"902","volume":"7","author":"R Ameri","year":"2019","unstructured":"Ameri R, Eyvazi M, Hoskova-Mayerova S (2019) Superring of polynomials over a hyperring. Mathamatics, MDPI 7:902","journal-title":"Mathamatics, MDPI"},{"key":"7372_CR2","doi-asserted-by":"publisher","first-page":"937","DOI":"10.1090\/S0002-9904-1948-09102-9","volume":"54","author":"SA Amitsur","year":"1948","unstructured":"Amitsur SA (1948) A generalization of a theorem on linear differential equations. Bull Am Math Soc 54:937\u2013941","journal-title":"Bull Am Math Soc"},{"key":"7372_CR3","unstructured":"Atamewoue S (2019) Algebraic hyperstructures and applications to coding theory. Thesis, University of Yaounde 1, Cameroon"},{"key":"7372_CR4","doi-asserted-by":"publisher","first-page":"147","DOI":"10.7151\/dmgaa.1277","volume":"37","author":"S Atamewoue","year":"2017","unstructured":"Atamewoue S, Ndjeya S, Str\u00fcngmann L, Lele C (2017) Codes over hyperfields. Discuss Math Gen Algebra Appl 37:147\u2013160","journal-title":"Discuss Math Gen Algebra Appl"},{"key":"7372_CR5","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1080\/09720529.2003.10697978","volume":"6","author":"RP Ciampi","year":"2003","unstructured":"Ciampi RP, Rota R (2003) Polynomials over multiplicative hyperrings. J Discrete Math Sci Cryptogr 6:217\u2013225","journal-title":"J Discrete Math Sci Cryptogr"},{"key":"7372_CR6","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1090\/S0002-9947-1963-0155851-X","volume":"109","author":"PM Cohn","year":"1963","unstructured":"Cohn PM (1963) Noncommutative unique factorization domains. Trans Am Math Soc 109:313\u2013331","journal-title":"Trans Am Math Soc"},{"key":"7372_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3714-1","volume-title":"Applications of hyperstructure theory","author":"P Corsini","year":"2003","unstructured":"Corsini P, Leoreanu V (2003) Applications of hyperstructure theory. Kluwer Academical Publications, Dordrecht"},{"key":"7372_CR8","unstructured":"Davvaz B, Leoreanu-Fotea V (2007) Hyperring theory and applications. International Academic Press, Palm Harbor, USA"},{"key":"7372_CR9","doi-asserted-by":"publisher","first-page":"197","DOI":"10.2307\/1968424","volume":"35","author":"N Jacobson","year":"1934","unstructured":"Jacobson N (1934) Non commutative polynomials and cyclic algebras. Ann Math 35:197\u2013208","journal-title":"Ann Math"},{"key":"7372_CR10","unstructured":"Jan\u010di\u0107-Ra\u0161ovi\u0107 S (2007) About the hyperring of polynomials. Ital J Pure Appl Math 21:223\u2013234"},{"key":"7372_CR11","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/BF00704588","volume":"10","author":"M Jimbo","year":"1985","unstructured":"Jimbo M (1985) A q-difference analog of $$U(g)$$ and the Yang-Baxter equation. Lett Math Phys 10:63\u201369","journal-title":"Lett Math Phys"},{"key":"7372_CR12","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1155\/S0161171283000265","volume":"6","author":"M Krasner","year":"1983","unstructured":"Krasner M (1983) A class of hyperrings and hyperfields. Int J Math Math Sci 6:307\u2013312","journal-title":"Int J Math Math Sci"},{"key":"7372_CR13","unstructured":"Krasner M (1956) Approximation des corps valu\u00e9s complets de caract\u00e9ristique $$p\\ne 0$$ par ceux de caract\u00e9ristique 0, Colloque d\u2019Alg\u00e8bre Sup\u00e9rieure. Bruxelles, Decembre"},{"key":"7372_CR14","unstructured":"Krasner M (1957) Centre Belge de recherches math\u00e9matiques, etablissement Ceuterick, Louvain, Librairie Gautier-Villars: Paris, France, pp 129\u2013206"},{"key":"7372_CR15","unstructured":"Lam Tsit-Yuen (2001) A first course in noncommutative rings. Springer-Verlag, ISBN 978-0-387-95325-0"},{"key":"7372_CR16","unstructured":"Marty F (1934) Sur une generalization de la notion de groupe, 8$$^{iem}$$ congres Math. Scandinaves, Stockholm, pp 45\u201349"},{"issue":"4","key":"7372_CR17","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1155\/S0161171285000813","volume":"8","author":"CG Massouros","year":"1985","unstructured":"Massouros CG (1985) Methods of constructing hyperfields. Int J Math Sci 8(4):725\u2013728. https:\/\/doi.org\/10.1155\/S0161171285000813","journal-title":"Int J Math Sci"},{"issue":"8","key":"7372_CR18","doi-asserted-by":"publisher","first-page":"1338","DOI":"10.3390\/math8081338","volume":"8","author":"G Massouros","year":"2020","unstructured":"Massouros G, Massouros C (2020) Hypercompositional algebra, computer science and geometry. Mathematics 8(8):1338. https:\/\/doi.org\/10.3390\/math8081338","journal-title":"Mathematics"},{"key":"7372_CR19","first-page":"4","volume":"271","author":"JD Mittas","year":"1970","unstructured":"Mittas JD (1970) Hypergroupes canoniques hypervalues. CR Acad Sci Paris 271:4\u20137","journal-title":"CR Acad Sci Paris"},{"key":"7372_CR20","first-page":"298","volume":"48","author":"JD Mittas","year":"1973","unstructured":"Mittas JD (1973) Sur certaines classes de structures hypercompositionnelles. Proc Acad Athens 48:298\u2013318","journal-title":"Proc Acad Athens"},{"key":"7372_CR21","unstructured":"Mittas JD (1990) Sur les structures hypercompositionnelles. In: Proceedings of the 4th international congress on AHA, Xanthi, Greece, 27\u201330 June. World Scientific: Singapore, pp 137\u2013147 (1991)"},{"key":"7372_CR22","doi-asserted-by":"publisher","first-page":"480","DOI":"10.2307\/1968173","volume":"34","author":"O Ore","year":"1933","unstructured":"Ore O (1933) Theory of non-commutative polynomials. Ann Math 34:480\u2013508","journal-title":"Ann Math"},{"key":"7372_CR23","doi-asserted-by":"publisher","first-page":"1644","DOI":"10.1016\/j.jsc.2007.11.008","volume":"44","author":"F Ulmer","year":"2009","unstructured":"Ulmer F, Boucher D (2009) Coding with skew polynomials rings. J Symb Comput 44:1644\u20131656","journal-title":"J Symb Comput"},{"key":"7372_CR24","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/s00200-007-0043-z","volume":"18","author":"F Ulmer","year":"2007","unstructured":"Ulmer F, Boucher D, Geiselmann W (2007) Skew cyclic codes. Appl Algebra Eng Commun Comput 18:379\u2013389","journal-title":"Appl Algebra Eng Commun Comput"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-07372-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-022-07372-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-07372-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,30]],"date-time":"2022-09-30T06:16:14Z","timestamp":1664518574000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-022-07372-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,16]]},"references-count":24,"journal-issue":{"issue":"21","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["7372"],"URL":"https:\/\/doi.org\/10.1007\/s00500-022-07372-6","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"type":"print","value":"1432-7643"},{"type":"electronic","value":"1433-7479"}],"subject":[],"published":{"date-parts":[[2022,8,16]]},"assertion":[{"value":"5 July 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 August 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 they have no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Yes.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}}]}}