{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T05:57:50Z","timestamp":1648879070276},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2008,2]]},"abstract":"<jats:p> Let K be a principal ideal domain, and A<jats:sub>n<\/jats:sub>, with n \u2265 3, be a finitely generated torsion-free abelian group of rank n. Let \u03a9 be a finite subset of KA<jats:sub>n<\/jats:sub>\\{0} and U(KA<jats:sub>n<\/jats:sub>) the group of units of KA<jats:sub>n<\/jats:sub>. For a multiplicative monoid P generated by U(KA<jats:sub>n<\/jats:sub>) and \u03a9, we prove that any generating set for [Formula: see text] contains infinitely many elements not in [Formula: see text]. Furthermore, we present a way of constructing elements of [Formula: see text] not in [Formula: see text] for n \u2265 3. In the case where K is not a field the aforementioned results hold for n \u2265 2. <\/jats:p>","DOI":"10.1142\/s0218196708004378","type":"journal-article","created":{"date-parts":[[2008,2,22]],"date-time":"2008-02-22T05:57:59Z","timestamp":1203659879000},"page":"165-180","source":"Crossref","is-referenced-by-count":0,"title":["A THEOREM ON MATRIX GROUPS"],"prefix":"10.1142","volume":"18","author":[{"given":"A. I.","family":"PAPISTAS","sequence":"first","affiliation":[{"name":"Faculty of Sciences, Department of Mathematics, Aristotle University of Thessaloniki, GR 541 21, Thessaloniki, Greece"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.2307\/2374056"},{"key":"rf2","first-page":"693","volume":"270","author":"Bachmuth S.","journal-title":"Trans. Amer. Math. Soc."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700018036"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511565878"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1998.7817"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1970-0260879-9"},{"key":"rf7","volume-title":"Encyclopedia of Mathematics and its Applications","volume":"20","author":"Lidl R.","year":"1983"},{"key":"rf8","volume-title":"Combinatorial Group Theory","author":"Magnus W.","year":"1976"},{"key":"rf9","volume":"49","author":"Papistas A. I.","journal-title":"Glasg. Math. J."},{"key":"rf11","series-title":"Pure and Applied Mathematics","volume-title":"Topics in group rings","volume":"50","author":"Sehgal S. I.","year":"1978"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61856-7"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196708004378","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:28:43Z","timestamp":1565116123000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196708004378"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,2]]},"references-count":11,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,2]]}},"alternative-id":["10.1142\/S0218196708004378"],"URL":"https:\/\/doi.org\/10.1142\/s0218196708004378","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,2]]}}}