{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T04:37:00Z","timestamp":1774413420718,"version":"3.50.1"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,6,14]],"date-time":"2021-06-14T00:00:00Z","timestamp":1623628800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,6,14]],"date-time":"2021-06-14T00:00:00Z","timestamp":1623628800000},"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":["Period Math Hung"],"published-print":{"date-parts":[[2022,3]]},"DOI":"10.1007\/s10998-021-00386-x","type":"journal-article","created":{"date-parts":[[2021,6,14]],"date-time":"2021-06-14T12:03:01Z","timestamp":1623672181000},"page":"18-30","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The algebraic and geometric classification of nilpotent right alternative algebras"],"prefix":"10.1007","volume":"84","author":[{"given":"Nurlan","family":"Ismailov","sequence":"first","affiliation":[]},{"given":"Ivan","family":"Kaygorodov","sequence":"additional","affiliation":[]},{"given":"Manat","family":"Mustafa","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,6,14]]},"reference":[{"issue":"6","key":"386_CR1","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1142\/S0218196719500437","volume":"29","author":"H Abdelwahab","year":"2019","unstructured":"H. Abdelwahab, A.J. Calder\u00f3n, I. Kaygorodov, The algebraic and geometric classification of nilpotent binary Lie algebras. Int. J. Algebra Comput. 29(6), 1113\u20131129 (2019)","journal-title":"Int. J. Algebra Comput."},{"issue":"2","key":"386_CR2","doi-asserted-by":"crossref","first-page":"318","DOI":"10.2307\/1969457","volume":"50","author":"A Albert","year":"1949","unstructured":"A. Albert, On the right alternative algebras. Ann. Math. 50(2), 318\u2013328 (1949)","journal-title":"Ann. Math."},{"issue":"3","key":"386_CR3","doi-asserted-by":"crossref","first-page":"408","DOI":"10.2307\/1969709","volume":"59","author":"A Albert","year":"1954","unstructured":"A. Albert, The structure of right alternative algebras. Ann. Math. 59(3), 408\u2013417 (1954)","journal-title":"Ann. Math."},{"issue":"2","key":"386_CR4","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1006\/jabr.1998.7714","volume":"214","author":"D Burde","year":"1999","unstructured":"D. Burde, C. Steinhoff, Classification of orbit closures of $$4$$-dimensional complex Lie algebras. J. Algebra 214(2), 729\u2013739 (1999)","journal-title":"J. Algebra"},{"key":"386_CR5","unstructured":"A. Calder\u00f3n Mart\u00e1n, A. Fern\u00e1ndez Ouaridi, I. Kaygorodov, The classification of bilinear maps with radical of codimension $$2$$, arXiv:1806.07009"},{"issue":"1","key":"386_CR6","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.laa.2011.06.037","volume":"436","author":"S Cical\u00e0","year":"2012","unstructured":"S. Cical\u00e0, W. De Graaf, C. Schneider, Six-dimensional nilpotent Lie algebras. Linear Algebra. Appl. 436(1), 163\u2013189 (2012)","journal-title":"Linear Algebra. Appl."},{"key":"386_CR7","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.jalgebra.2016.06.011","volume":"464","author":"I Darijani","year":"2016","unstructured":"I. Darijani, H. Usefi, The classification of $$5$$-dimensional $$p$$-nilpotent restricted Lie algebras over perfect fields, I. J. Algebra 464, 97\u2013140 (2016)","journal-title":"J. Algebra"},{"issue":"2","key":"386_CR8","doi-asserted-by":"crossref","first-page":"640","DOI":"10.1016\/j.jalgebra.2006.08.006","volume":"309","author":"W De Graaf","year":"2007","unstructured":"W. De Graaf, Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not $$2$$. J. Algebra 309(2), 640\u2013653 (2007)","journal-title":"J. Algebra"},{"issue":"1","key":"386_CR9","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1142\/S0218196718500078","volume":"28","author":"W De Graaf","year":"2018","unstructured":"W. De Graaf, Classification of nilpotent associative algebras of small dimension. Int. J. Algebra Comput. 28(1), 133\u2013161 (2018)","journal-title":"Int. J. Algebra Comput."},{"issue":"3","key":"386_CR10","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1080\/00927872.2016.1172626","volume":"45","author":"I Demir","year":"2017","unstructured":"I. Demir, K. Misra, E. Stitzinger, On classification of four-dimensional nilpotent Leibniz algebras. Commun. Algebra 45(3), 1012\u20131018 (2017)","journal-title":"Commun. Algebra"},{"issue":"1","key":"386_CR11","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1080\/00927872.2019.1635612","volume":"48","author":"I Gorshkov","year":"2020","unstructured":"I. Gorshkov, I. Kaygorodov, M. Khrypchenko, The geometric classification of nilpotent Tortkara algebras. Commun. Algebra 48(1), 204\u2013209 (2020)","journal-title":"Commun. Algebra"},{"issue":"8","key":"386_CR12","doi-asserted-by":"crossref","first-page":"3608","DOI":"10.1080\/00927872.2020.1742347","volume":"48","author":"I Gorshkov","year":"2020","unstructured":"I. Gorshkov, I. Kaygorodov, M. Khrypchenko, The algebraic classification of nilpotent Tortkara algebras. Commun. Algebra 48(8), 3608\u20133623 (2020)","journal-title":"Commun. Algebra"},{"key":"386_CR13","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/0021-8693(88)90093-2","volume":"112","author":"F Grunewald","year":"1988","unstructured":"F. Grunewald, J. O\u2019Halloran, Varieties of nilpotent Lie algebras of dimension less than six. J. Algebra 112, 315\u2013325 (1988)","journal-title":"J. Algebra"},{"key":"386_CR14","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/0021-8693(88)90199-8","volume":"116","author":"F Grunewald","year":"1988","unstructured":"F. Grunewald, J. O\u2019Halloran, A Characterization of orbit closure and applications. J. Algebra 116, 163\u2013175 (1988)","journal-title":"J. Algebra"},{"key":"386_CR15","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.laa.2016.01.015","volume":"494","author":"A Hegazi","year":"2016","unstructured":"A. Hegazi, H. Abdelwahab, Classification of five-dimensional nilpotent Jordan algebras. Linear Algebra Appl. 494, 165\u2013218 (2016)","journal-title":"Linear Algebra Appl."},{"issue":"4","key":"386_CR16","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1007\/s13366-016-0292-8","volume":"57","author":"A Hegazi","year":"2016","unstructured":"A. Hegazi, H. Abdelwahab, Is it possible to find for any $$n, m \\in {\\mathbb{N}}$$ a Jordan algebra of nilpotency type $$(n,1, m)$$? Beitrage zur Algebra und Geometrie 57(4), 859\u2013880 (2016)","journal-title":"Beitrage zur Algebra und Geometrie"},{"key":"386_CR17","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.laa.2016.04.029","volume":"505","author":"A Hegazi","year":"2016","unstructured":"A. Hegazi, H. Abdelwahab, M.A. Calder\u00f3n, The classification of $$n$$-dimensional non-Lie Malcev algebras with $$(n-4)$$-dimensional annihilator. Linear Algebra Appl. 505, 32\u201356 (2016)","journal-title":"Linear Algebra Appl."},{"issue":"2","key":"386_CR18","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1007\/BF01978883","volume":"25","author":"I Isaev","year":"1986","unstructured":"I. Isaev, Finite-dimensional right alternative algebras generating non-finite-basable varieties. Algebra Log. 25(2), 136\u2013153 (1986)","journal-title":"Algebra Log."},{"key":"386_CR19","doi-asserted-by":"crossref","unstructured":"N. Ismailov, I. Kaygorodov, F. Mashurov, The algebraic and geometric classification of nilpotent assosymmetric algebras. Algebras Represent. Theory, 24(1), 135\u2013148 (2021)","DOI":"10.1007\/s10468-019-09935-y"},{"issue":"5","key":"386_CR20","doi-asserted-by":"crossref","first-page":"1850035","DOI":"10.1142\/S0129167X18500350","volume":"29","author":"N Ismailov","year":"2018","unstructured":"N. Ismailov, I. Kaygorodov, Yu. Volkov, The geometric classification of Leibniz algebras. Int. J. Math. 29(5), 1850035 (2018)","journal-title":"Int. J. Math."},{"issue":"3","key":"386_CR21","doi-asserted-by":"crossref","first-page":"539","DOI":"10.4153\/S0008439519000018","volume":"62","author":"N Ismailov","year":"2019","unstructured":"N. Ismailov, I. Kaygorodov, Yu. Volkov, Degenerations of Leibniz and anticommutative algebras. Can. Math. Bull. 62(3), 539\u2013549 (2019)","journal-title":"Can. Math. Bull."},{"key":"386_CR22","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498821502029","author":"D Jumaniyozov","year":"2020","unstructured":"D. Jumaniyozov, I. Kaygorodov, A. Khudoyberdiyev, The algebraic and geometric classification of nilpotent noncommutative Jordan algebras. J. Algebra Appl. (2020). https:\/\/doi.org\/10.1142\/S0219498821502029","journal-title":"J. Algebra Appl."},{"key":"386_CR23","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.geomphys.2019.04.016","volume":"143","author":"I Karimjanov","year":"2019","unstructured":"I. Karimjanov, I. Kaygorodov, K. Khudoyberdiyev, The algebraic and geometric classification of nilpotent Novikov algebras. J. Geom. Phys. 143, 11\u201321 (2019)","journal-title":"J. Geom. Phys."},{"issue":"8","key":"386_CR24","doi-asserted-by":"crossref","first-page":"106337","DOI":"10.1016\/j.jpaa.2020.106337","volume":"224","author":"I Kaygorodov","year":"2020","unstructured":"I. Kaygorodov, M. Khrypchenko, S. Lopes, The algebraic and geometric classification of nilpotent anticommutative algebras. J. Pure. Appl. Algebra 224(8), 106337 (2020)","journal-title":"J. Pure. Appl. Algebra"},{"key":"386_CR25","doi-asserted-by":"crossref","first-page":"1190","DOI":"10.1016\/j.jalgebra.2020.06.013","volume":"560","author":"I Kaygorodov","year":"2020","unstructured":"I. Kaygorodov, S. Lopes, P. P\u00e1ez-Guill\u00e1n, Non-associative central extensions of null-filiform associative algebras. J. Algebra 560, 1190\u20131210 (2020)","journal-title":"J. Algebra"},{"issue":"4","key":"386_CR26","doi-asserted-by":"crossref","first-page":"1632","DOI":"10.1080\/00927872.2019.1691581","volume":"48","author":"I Kaygorodov","year":"2020","unstructured":"I. Kaygorodov, S. Lopes, Yu. Popov, Degenerations of nilpotent associative commutative algebras. Commun. Algebra 48(4), 1632\u20131639 (2020)","journal-title":"Commun. Algebra"},{"key":"386_CR27","doi-asserted-by":"crossref","unstructured":"I. Kaygorodov, P. Paez-Guill\u00e1n, V. Voronin, The algebraic and geometric classification of nilpotent bicommutative algebras. Algebras Represent. Theory 23(6), 2331\u20132347 (2020)","DOI":"10.1007\/s10468-019-09944-x"},{"key":"386_CR28","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.jalgebra.2016.02.016","volume":"456","author":"I Kaygorodov","year":"2016","unstructured":"I. Kaygorodov, Yu. Popov, A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations. J. Algebra 456, 323\u2013347 (2016)","journal-title":"J. Algebra"},{"issue":"4","key":"386_CR29","doi-asserted-by":"crossref","first-page":"704","DOI":"10.1080\/03081087.2017.1319457","volume":"66","author":"I Kaygorodov","year":"2018","unstructured":"I. Kaygorodov, Yu. Popov, A. Pozhidaev, Yu. Volkov, Degenerations of Zinbiel and nilpotent Leibniz algebras. Linear Multilinear Algebra 66(4), 704\u2013716 (2018)","journal-title":"Linear Multilinear Algebra"},{"issue":"4","key":"386_CR30","doi-asserted-by":"crossref","first-page":"819","DOI":"10.4153\/S0008414X18000056","volume":"71","author":"I Kaygorodov","year":"2019","unstructured":"I. Kaygorodov, Yu. Volkov, The variety of $$2$$-dimensional algebras over an algebraically closed field. Can. J. Math. 71(4), 819\u2013842 (2019)","journal-title":"Can. J. Math."},{"issue":"3","key":"386_CR31","doi-asserted-by":"crossref","first-page":"485","DOI":"10.17323\/1609-4514-2019-19-3-485-521","volume":"19","author":"I Kaygorodov","year":"2019","unstructured":"I. Kaygorodov, Yu. Volkov, Complete classification of algebras of level two. Mosc. Mathe. J. 19(3), 485\u2013521 (2019)","journal-title":"Mosc. Mathe. J."},{"issue":"2","key":"386_CR32","doi-asserted-by":"crossref","first-page":"021701","DOI":"10.1063\/1.5119393","volume":"61","author":"I Kaygorodov","year":"2020","unstructured":"I. Kaygorodov, Yu. Volkov, Degenerations of Filippov algebras. J. Math. Phys. 61(2), 021701 (2020)","journal-title":"J. Math. Phys."},{"issue":"1","key":"386_CR33","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF01297739","volume":"27","author":"G Mazzola","year":"1979","unstructured":"G. Mazzola, The algebraic and geometric classification of associative algebras of dimension five. Manuscr. Math. 27(1), 81\u2013101 (1979)","journal-title":"Manuscr. Math."},{"issue":"2","key":"386_CR34","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/BF02566686","volume":"55","author":"G Mazzola","year":"1980","unstructured":"G. Mazzola, Generic finite schemes and Hochschild cocycles. Comment. Math. Helv. 55(2), 267\u2013293 (1980)","journal-title":"Comment. Math. Helv."},{"issue":"6","key":"386_CR35","first-page":"682","volume":"16","author":"I Miheev","year":"1977","unstructured":"I. Miheev, Simple right alternative rings. Algebra Log. 16(6), 682\u2013710 (1977)","journal-title":"Algebra Log."},{"issue":"2","key":"386_CR36","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1007\/BF00967573","volume":"17","author":"S Pchelintsev","year":"1976","unstructured":"S. Pchelintsev, The locally nilpotent radical in certain classes of right alternative rings. Sib. Math. J. 17(2), 340\u2013360 (1976)","journal-title":"Sib. Math. J."},{"issue":"4","key":"386_CR37","doi-asserted-by":"crossref","first-page":"754","DOI":"10.1007\/BF02106619","volume":"35","author":"S Pchelintsev","year":"1994","unstructured":"S. Pchelintsev, Right alternative Malcev-admissible nil algebras of bounded index. Sib. Math. J. 35(4), 754\u2013759 (1994)","journal-title":"Sib. Math. J."},{"issue":"5\u20136","key":"386_CR38","doi-asserted-by":"crossref","first-page":"756","DOI":"10.1134\/S000143461305012X","volume":"93","author":"S Pchelintsev","year":"2013","unstructured":"S. Pchelintsev, On the commutator nilpotency step of strictly $$(-1,1)$$-algebras. Math. Notes 93(5\u20136), 756\u2013762 (2013)","journal-title":"Math. Notes"},{"key":"386_CR39","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1016\/j.jalgebra.2019.10.023","volume":"546","author":"S Pchelintsev","year":"2020","unstructured":"S. Pchelintsev, O. Shashkov, Linearly generated singular superalgebras. J. Algebra 546, 580\u2013603 (2020)","journal-title":"J. Algebra"},{"key":"386_CR40","doi-asserted-by":"crossref","first-page":"3493","DOI":"10.1080\/00927879008824088","volume":"18","author":"C Seeley","year":"1990","unstructured":"C. Seeley, Degenerations of 6-dimensional nilpotent Lie algebras over $${\\mathbb{C}}$$. Commun. Algebra 18, 3493\u20133505 (1990)","journal-title":"Commun. Algebra"},{"issue":"5","key":"386_CR41","first-page":"A241","volume":"286","author":"T Skjelbred","year":"1978","unstructured":"T. Skjelbred, T. Sund, Sur la classification des algebres de Lie nilpotentes, C. R. Acad. Sci. Paris Ser. A-B 286(5), A241\u2013A242 (1978)","journal-title":"R. Acad. Sci. Paris Ser. A-B"},{"issue":"1","key":"386_CR42","first-page":"73","volume":"18","author":"V Skosyrskiy","year":"1979","unstructured":"V. Skosyrskiy, Nilpotency in Jordan and right alternative algebras. Algebra Log. 18(1), 73\u201385 (1979)","journal-title":"Algebra Log."},{"issue":"2","key":"386_CR43","first-page":"205","volume":"24","author":"V Skosyrskiy","year":"1985","unstructured":"V. Skosyrskiy, Right alternative algebras with minimality condition for right ideals. Algebra Log. 24(2), 205\u2013210 (1985)","journal-title":"Algebra Log."},{"issue":"2","key":"386_CR44","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1016\/0021-8693(77)90316-7","volume":"48","author":"A Thedy","year":"1977","unstructured":"A. Thedy, Nil-semisimple right alternative algebras. J. Algebra 48(2), 390\u2013400 (1977)","journal-title":"J. Algebra"},{"issue":"3","key":"386_CR45","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1090\/S0002-9939-1978-0509228-1","volume":"72","author":"A Thedy","year":"1978","unstructured":"A. Thedy, Right alternative algebras and Wedderburn principal theorem. Proc. Am. Math. Soc. 72(3), 427\u2013435 (1978)","journal-title":"Proc. Am. Math. Soc."},{"key":"386_CR46","first-page":"130","volume-title":"The Word Problem for Metabelian Right-Alternative Algebras, Model-Theoretic Algebra","author":"U Umirbaev","year":"1989","unstructured":"U. Umirbaev, The Word Problem for Metabelian Right-Alternative Algebras, Model-Theoretic Algebra (Kazakh. Gos. Univ, Alma Ata, 1989), pp. 130\u2013139"},{"key":"386_CR47","first-page":"120","volume-title":"The Word Problem for Jordan and Right-Alternative Algebras, Some Questions and Problems in Analysis and Algebra","author":"U Umirbaev","year":"1985","unstructured":"U. Umirbaev, The Word Problem for Jordan and Right-Alternative Algebras, Some Questions and Problems in Analysis and Algebra (Novosibirsk. Gos. Univ, Novosibirsk, 1985), pp. 120\u2013127"},{"key":"386_CR48","doi-asserted-by":"publisher","DOI":"10.1080\/03081087.2020.1715333","author":"Y Volkov","year":"2020","unstructured":"Y. Volkov, Anticommutative Engel algebras of the first five levels. Linear Multilinear Algebra (2020). https:\/\/doi.org\/10.1080\/03081087.2020.1715333","journal-title":"Linear Multilinear Algebra"},{"key":"386_CR49","unstructured":"Y. Volkov, $$n$$-ary algebras of the first level, arXiv:1910.10200"},{"issue":"1","key":"386_CR50","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1090\/S0002-9947-1992-1069751-2","volume":"334","author":"P Zusmanovich","year":"1992","unstructured":"P. Zusmanovich, Central extensions of current algebras. Trans. Am. Math. Soc. 334(1), 143\u2013152 (1992)","journal-title":"Trans. Am. Math. Soc."}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-021-00386-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10998-021-00386-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-021-00386-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T09:05:51Z","timestamp":1644915951000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10998-021-00386-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,14]]},"references-count":50,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,3]]}},"alternative-id":["386"],"URL":"https:\/\/doi.org\/10.1007\/s10998-021-00386-x","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"value":"0031-5303","type":"print"},{"value":"1588-2829","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,14]]},"assertion":[{"value":"10 August 2020","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 June 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}