{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:49:03Z","timestamp":1775465343939,"version":"3.50.1"},"reference-count":30,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"crossref","award":["21-11-00286"],"award-info":[{"award-number":["21-11-00286"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2021,11]]},"abstract":"<jats:p> We show that the right ideal of a Novikov algebra generated by the square of a right nilpotent subalgebra is nilpotent. We also prove that a [Formula: see text]-graded Novikov algebra [Formula: see text] over a field [Formula: see text] with solvable [Formula: see text]-component [Formula: see text] is solvable, where [Formula: see text] is a finite additive abelean group and the characteristic of [Formula: see text] does not divide the order of the group [Formula: see text]. We also show that any Novikov algebra [Formula: see text] with a finite solvable group of automorphisms [Formula: see text] is solvable if the algebra of invariants [Formula: see text] is solvable. <\/jats:p>","DOI":"10.1142\/s0218196721500491","type":"journal-article","created":{"date-parts":[[2021,7,8]],"date-time":"2021-07-08T09:57:46Z","timestamp":1625738266000},"page":"1405-1418","source":"Crossref","is-referenced-by-count":10,"title":["On the solvability of graded Novikov algebras"],"prefix":"10.1142","volume":"31","author":[{"given":"Ualbai","family":"Umirbaev","sequence":"first","affiliation":[{"name":"Department of Mathematics, Wayne State University, Detroit, MI 48202, USA"},{"name":"Department of Mathematics, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan"},{"name":"Institute of Mathematics of the SB of RAS, Novosibirsk 630090, Russia"},{"name":"Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Viktor","family":"Zhelyabin","sequence":"additional","affiliation":[{"name":"Institute of Mathematics of the SB of RAS, Novosibirsk 630090, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,7,7]]},"reference":[{"issue":"5","key":"S0218196721500491BIB001","first-page":"1036","volume":"283","author":"Balinskii I. 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