{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,19]],"date-time":"2023-04-19T09:58:38Z","timestamp":1681898318596},"reference-count":13,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2014,9,1]],"date-time":"2014-09-01T00:00:00Z","timestamp":1409529600000},"content-version":"unspecified","delay-in-days":243,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Differential difference algebras, introduced by Mansfield and Szanto, arose naturally from differential difference equations. In this paper, we investigate the Gelfand\u2013Kirillov dimension of differential difference algebras. We give a lower bound of the Gelfand\u2013Kirillov dimension of a differential difference algebra and a sufficient condition under which the lower bound is reached; we also find an upper bound of this Gelfand\u2013Kirillov dimension under some specific conditions and construct an example to show that this upper bound cannot be sharpened any further.<\/jats:p>","DOI":"10.1112\/s1461157014000102","type":"journal-article","created":{"date-parts":[[2014,9,23]],"date-time":"2014-09-23T09:10:45Z","timestamp":1411463445000},"page":"485-495","source":"Crossref","is-referenced-by-count":3,"title":["Gelfand\u2013Kirillov dimension of differential difference algebras"],"prefix":"10.1112","volume":"17","author":[{"given":"Yang","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Xiangui","family":"Zhao","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2014,9,1]]},"reference":[{"key":"S1461157014000102_r12","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/030"},{"key":"S1461157014000102_r3","doi-asserted-by":"publisher","DOI":"10.1080\/00927879608825702"},{"key":"S1461157014000102_r6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0783-2"},{"key":"S1461157014000102_r9","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(82)90285-X"},{"key":"S1461157014000102_r8","doi-asserted-by":"publisher","DOI":"10.1145\/860854.860895"},{"key":"S1461157014000102_r13","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-97-03602-2"},{"key":"S1461157014000102_r10","doi-asserted-by":"publisher","DOI":"10.1145\/860854.860897"},{"key":"S1461157014000102_r4","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2000.0643"},{"key":"S1461157014000102_r5","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(08)80003-X"},{"key":"S1461157014000102_r11","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-2985-2_18"},{"key":"S1461157014000102_r2","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45539-6_27"},{"key":"S1461157014000102_r1","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1988.131.13"},{"key":"S1461157014000102_r7","volume-title":"Growth of algebras and Gelfand\u2013Kirillov dimension","author":"Krause","year":"2000"}],"container-title":["LMS Journal of Computation and Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1461157014000102","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T21:59:54Z","timestamp":1555970394000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1461157014000102\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014]]}},"alternative-id":["S1461157014000102"],"URL":"https:\/\/doi.org\/10.1112\/s1461157014000102","relation":{},"ISSN":["1461-1570"],"issn-type":[{"value":"1461-1570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}