{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:42:18Z","timestamp":1775464938409,"version":"3.50.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2016,3]]},"abstract":"<jats:p> Let [Formula: see text] be the polynomial algebra over a field [Formula: see text] of characteristic zero in the variables [Formula: see text] and [Formula: see text] be the left-symmetric Witt algebra of all derivations of [Formula: see text] [D. Burde, Left-symmetric algebras, or pre-Lie algebras in geometry and physics, Cent. Eur. J. Math. 4(3) (2006) 323\u2013357]. We describe all right operator identities of [Formula: see text] and prove that the set of all algebras [Formula: see text], where [Formula: see text], generates the variety of all left-symmetric algebras. We also describe a class of general (not only right operator) identities for [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s021819671650017x","type":"journal-article","created":{"date-parts":[[2016,2,18]],"date-time":"2016-02-18T05:09:53Z","timestamp":1455772193000},"page":"435-450","source":"Crossref","is-referenced-by-count":8,"title":["Identities of the left-symmetric Witt algebras"],"prefix":"10.1142","volume":"26","author":[{"given":"Daniyar","family":"Kozybaev","sequence":"first","affiliation":[{"name":"Eurasian National University, Astana, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ualbai","family":"Umirbaev","sequence":"additional","affiliation":[{"name":"Eurasian National University, Astana, Kazakhstan and Wayne State University, Detroit, MI 48202, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,3,16]]},"reference":[{"key":"S021819671650017XBIB001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1950-0036751-9"},{"key":"S021819671650017XBIB002","doi-asserted-by":"publisher","DOI":"10.2478\/s11533-006-0014-9"},{"key":"S021819671650017XBIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s00200-012-0180-x"},{"key":"S021819671650017XBIB004","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1999.8109"},{"key":"S021819671650017XBIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2014.12.023"},{"key":"S021819671650017XBIB007","doi-asserted-by":"publisher","DOI":"10.1142\/S1793557108000230"},{"issue":"2","key":"S021819671650017XBIB008","first-page":"66","volume":"2","author":"Makar-Limanov L.","year":"2011","journal-title":"TWMS J. Pure Appl. Math."},{"key":"S021819671650017XBIB009","first-page":"393","volume":"10","author":"Maltsev Yu.","year":"1971","journal-title":"Algebra i Logika"},{"key":"S021819671650017XBIB010","series-title":"Translations of Mathematical Monographs","doi-asserted-by":"crossref","DOI":"10.1090\/mmono\/138","volume-title":"Identities of Algebras and Their Representations","volume":"138","author":"Razmyslov Yu. P.","year":"1994"},{"key":"S021819671650017XBIB011","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1994.1088"},{"issue":"6","key":"S021819671650017XBIB013","first-page":"1294","volume":"292","author":"Zelmanov E. I.","year":"1987","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"S021819671650017XBIB015","volume-title":"Rings That are Nearly Associative","author":"Zhevlakov K. A.","year":"1982"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819671650017X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:27:43Z","timestamp":1565130463000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819671650017X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3]]},"references-count":12,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2016,3,16]]},"published-print":{"date-parts":[[2016,3]]}},"alternative-id":["10.1142\/S021819671650017X"],"URL":"https:\/\/doi.org\/10.1142\/s021819671650017x","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3]]}}}