{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T20:45:28Z","timestamp":1773261928146,"version":"3.50.1"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2019,8]]},"abstract":"<jats:p>A polynomial automorphism of [Formula: see text] over a field of characteristic zero is called co-tame if, together with the affine subgroup, it generates the entire tame subgroup. We prove some new classes of automorphisms of [Formula: see text], including nonaffine [Formula: see text]-triangular automorphisms, are co-tame. Of particular interest, if [Formula: see text], we show that the statement \u201cEvery [Formula: see text]-triangular automorphism is either affine or co-tame\u201d is true if and only if [Formula: see text]; this improves upon positive results of Bodnarchuk (for [Formula: see text], in any dimension [Formula: see text]) and negative results of the authors (for [Formula: see text], [Formula: see text]). The main technical tool we introduce is a class of maps we term translation degenerate automorphisms; we show that all of these are either affine or co-tame, a result that may be of independent interest in the further study of co-tame\u00a0automorphisms.<\/jats:p>","DOI":"10.1142\/s0218196719500292","type":"journal-article","created":{"date-parts":[[2019,1,31]],"date-time":"2019-01-31T08:20:48Z","timestamp":1548922848000},"page":"803-825","source":"Crossref","is-referenced-by-count":3,"title":["Co-tame polynomial automorphisms"],"prefix":"10.1142","volume":"29","author":[{"given":"Eric","family":"Edo","sequence":"first","affiliation":[{"name":"ISEA, University of New Caledonia, New Caledonia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Drew","family":"Lewis","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of South Alabama, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,7,8]]},"reference":[{"key":"S0218196719500292BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196705002621"},{"key":"S0218196719500292BIB003","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2012.700981"},{"key":"S0218196719500292BIB004","doi-asserted-by":"publisher","DOI":"10.1307\/mmj\/1441116658"},{"key":"S0218196719500292BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00031-010-9095-4"},{"key":"S0218196719500292BIB006","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1515\/crll.1942.184.161","volume":"184","author":"Jung H.","year":"1942","journal-title":"J. Reine Angew. Math."},{"key":"S0218196719500292BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00031-017-9427-8"},{"key":"S0218196719500292BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-014-1138-z"},{"key":"S0218196719500292BIB011","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-03-00440-5"},{"key":"S0218196719500292BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(89)90158-8"},{"key":"S0218196719500292BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8440-2"},{"key":"S0218196719500292BIB014","series-title":"Polynomial Automorphisms and Related Topics","volume-title":"Polynomial Automorphism Groups","volume":"119","author":"Wright D.","year":"2007"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196719500292","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,11]],"date-time":"2022-09-11T05:09:38Z","timestamp":1662872978000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196719500292"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,8]]},"references-count":11,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2019,7,8]]},"published-print":{"date-parts":[[2019,8]]}},"alternative-id":["10.1142\/S0218196719500292"],"URL":"https:\/\/doi.org\/10.1142\/s0218196719500292","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,8]]}}}