{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T21:04:14Z","timestamp":1776200654385,"version":"3.50.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2003,6]]},"abstract":"<jats:p>In 1987, Squier defined the notion of finite derivation type for a finitely presented monoid. To do this, he associated a 2-complex to the presentation. The monoid then has finite derivation type if, modulo the action of the free monoid ring, the 1-dimensional homotopy of this complex is finitely generated. Cremanns and Otto showed that finite derivation type implies the homological finiteness condition left FP<jats:sub>3<\/jats:sub>, and when the monoid is a group, these two properties are equivalent. In this paper we define a new version of finite derivation type, based on homological information, together with an extension of this finite derivation type to higher dimensions, and show connections to homological type FP<jats:sub>n<\/jats:sub>for both monoids and groups.<\/jats:p>","DOI":"10.1142\/s0218196703001407","type":"journal-article","created":{"date-parts":[[2003,8,20]],"date-time":"2003-08-20T09:30:13Z","timestamp":1061371813000},"page":"341-359","source":"Crossref","is-referenced-by-count":7,"title":["Homological Finite Derivation Type"],"prefix":"10.1142","volume":"13","author":[{"given":"Juan M.","family":"Alonso","sequence":"first","affiliation":[{"name":"SICS Swedish Institute of Computer Science Box 1263, SE-164 29 Kista, Sweden"}]},{"given":"Susan M.","family":"Hermiller","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Nebraska, Lincoln, NE 68588-0323, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(94)90069-8"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9327-6"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/24.4.340"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1994.1039"},{"key":"rf5","first-page":"155","volume":"18","author":"Cremanns R.","journal-title":"J. Symbolic Comput."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(97)00095-9"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196701000577"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(94)00043-I"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196795000252"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1017\/S0017089599970179"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(94)90175-9"},{"key":"rf12","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1142\/S0218196700000200","volume":"10","author":"Wang X.","journal-title":"Internat J. Algebra Comput."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196703001407","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,25]],"date-time":"2020-03-25T07:44:02Z","timestamp":1585122242000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196703001407"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,6]]},"references-count":12,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,6]]}},"alternative-id":["10.1142\/S0218196703001407"],"URL":"https:\/\/doi.org\/10.1142\/s0218196703001407","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,6]]}}}