{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T09:46:41Z","timestamp":1773395201157,"version":"3.50.1"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2004,8]]},"abstract":"<jats:p> We consider algebras over a field with generators x<jats:sub>1<\/jats:sub>,x<jats:sub>2<\/jats:sub>,\u2026,x<jats:sub>n<\/jats:sub> subject to [Formula: see text] square-free relations x<jats:sub>i<\/jats:sub>x<jats:sub>j<\/jats:sub>=x<jats:sub>k<\/jats:sub>x<jats:sub>l<\/jats:sub> in which every product x<jats:sub>p<\/jats:sub>x<jats:sub>q<\/jats:sub>, p\u2260q, appears in one of the relations. The work of Gateva-Ivanova and Van den Bergh, motivated in particular by the study of set theoretic solutions of the Yang\u2013Baxter equation, provided an important class of such algebras. In this special case the presentation satisfies the so-called cyclic condition that became an essential combinatorial tool in proving that these algebras share many strong ring theoretic properties of polynomial algebras in commuting variables. In this paper we describe the structure of algebras on four generators satisfying the cyclic condition. The emphasis is on some new unexpected features, not present in the motivating special classes. <\/jats:p>","DOI":"10.1142\/s0218196704001864","type":"journal-article","created":{"date-parts":[[2004,8,26]],"date-time":"2004-08-26T11:56:19Z","timestamp":1093521379000},"page":"479-498","source":"Crossref","is-referenced-by-count":3,"title":["QUADRATIC ALGEBRAS OF SKEW TYPE SATISFYING THE CYCLIC CONDITION"],"prefix":"10.1142","volume":"14","author":[{"given":"ERIC","family":"JESPERS","sequence":"first","affiliation":[{"name":"Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JAN","family":"OKNI\u0143SKI","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"The Algebraic Theory of Semigroups","author":"Clifford A. H.","year":"1961"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-99-10007-X"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1994-1173854-3"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1996.0348"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1997.7399"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2003.06.005"},{"key":"rf8","volume-title":"An Introduction to Noncommutative Noetherian Rings","author":"Goodearl K. R.","year":"1989"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1997.7292"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011433816487"},{"key":"rf11","series-title":"Graduate Studies in Mathematics","volume-title":"Growth of Algebras and Gelfand\u2013Kirillov Dimension","volume":"22","author":"Krause G. R.","year":"2000"},{"key":"rf12","volume-title":"Noncommutative Noetherian Rings","author":"McConnell J. C.","year":"1987"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1993.1255"},{"key":"rf14","volume-title":"Semigroup Algebras","author":"Okni\u0144ski J.","year":"1991"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/s002220050065"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196704001864","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:40:51Z","timestamp":1565185251000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196704001864"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,8]]},"references-count":14,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2004,8]]}},"alternative-id":["10.1142\/S0218196704001864"],"URL":"https:\/\/doi.org\/10.1142\/s0218196704001864","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,8]]}}}