{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T14:37:10Z","timestamp":1778683030851,"version":"3.51.4"},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,5]]},"abstract":"<jats:p> A graded associative algebra generated by m elements of degree one is called Golod\u2013Shafarevich (GS) if it is presented with less than m<jats:sup>2<\/jats:sup>\/4 relators of degree at least two. We explore conditions under which subalgebras of graded GS algebras are themselves GS. We prove that infinitely many Veronese powers of an algebra presented by m generators and r relators are GS if [Formula: see text]. For quadratic algebras, the bound is improved to [Formula: see text]. We also show that if A is a generic quadratic algebra presented by m generators and r relators, then all Veronese powers of A are GS if [Formula: see text], and all but finitely many Veronese powers of A are not GS if [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196709005196","type":"journal-article","created":{"date-parts":[[2009,5,19]],"date-time":"2009-05-19T06:51:17Z","timestamp":1242715877000},"page":"423-442","source":"Crossref","is-referenced-by-count":8,"title":["SUBALGEBRAS OF GOLOD\u2013SHAFAREVICH ALGEBRAS"],"prefix":"10.1142","volume":"19","author":[{"given":"THOMAS","family":"VODEN","sequence":"first","affiliation":[{"name":"Glendale College, 1500 North Verdugo Road, Glendale, CA 91208, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf2","first-page":"261","volume":"28","author":"Golod E. S.","journal-title":"Izvestia Akad. Nauk SSSR, Ser. Mat."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1969-0249461-9"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.2307\/2006956"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1090\/ulect\/037"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.2307\/1970630"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1380-2_7"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196709005196","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T09:34:58Z","timestamp":1565170498000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196709005196"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5]]},"references-count":6,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,5]]}},"alternative-id":["10.1142\/S0218196709005196"],"URL":"https:\/\/doi.org\/10.1142\/s0218196709005196","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,5]]}}}