{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T12:32:52Z","timestamp":1648989172165},"reference-count":15,"publisher":"Wiley","license":[{"start":{"date-parts":[[2010,2,1]],"date-time":"2010-02-01T00:00:00Z","timestamp":1264982400000},"content-version":"unspecified","delay-in-days":762,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2008]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>A<\/jats:italic> be a finite dimensional algebra over a finite field <jats:italic>F<\/jats:italic>. Condensing an <jats:italic>A<\/jats:italic>-module <jats:italic>V<\/jats:italic> with two different idempotents <jats:italic>e<\/jats:italic> and <jats:italic>e<\/jats:italic>\u2032 leads to the problem that to compare the composition series of <jats:italic>V e<\/jats:italic> and <jats:italic>V e<\/jats:italic>\u2032, we need to match the composition factors of both modules. In other words, given a composition factor <jats:italic>S<\/jats:italic> of <jats:italic>V e<\/jats:italic>, we have to find a composition factor <jats:italic>S<\/jats:italic>\u2032 of <jats:italic>V e<\/jats:italic>\u2032 such that there exists a composition factor \u015c of <jats:italic>V<\/jats:italic> with <jats:italic>\u015c e<\/jats:italic> \u2245 <jats:italic>S<\/jats:italic> and <jats:italic>\u015c e<\/jats:italic>\u2032 \u2245 <jats:italic>S<\/jats:italic>\u2032, or prove that no such <jats:italic>S<\/jats:italic>\u2032 exists. In this note, we present a computationally tractable solution to this problem.<\/jats:p>","DOI":"10.1112\/s1461157000000577","type":"journal-article","created":{"date-parts":[[2011,4,20]],"date-time":"2011-04-20T05:35:08Z","timestamp":1303277708000},"page":"213-222","source":"Crossref","is-referenced-by-count":2,"title":["Matching Simple Modules of Condensed Algebras"],"prefix":"10.1112","volume":"11","author":[{"given":"Felix","family":"Noeske","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2010,2,1]]},"reference":[{"key":"S1461157000000577_ref015","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.2001.0459"},{"key":"S1461157000000577_ref014","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(08)80076-4"},{"key":"S1461157000000577_ref008","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511565830.018"},{"key":"S1461157000000577_ref010","first-page":"309","volume-title":"Computational methods for representations of groups and algebras","author":"M\u00fcller","year":"1997"},{"key":"S1461157000000577_ref011","unstructured":"11. 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Lux K. , Neunh\u00f6ffer M. and Noeske F. , \u2018Condensation of homomorphism spaces\u2019, in preparation."},{"key":"S1461157000000577_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2006.06.020"}],"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\/S1461157000000577","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T19:48:02Z","timestamp":1559936882000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1461157000000577\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008]]},"references-count":15,"alternative-id":["S1461157000000577"],"URL":"https:\/\/doi.org\/10.1112\/s1461157000000577","relation":{},"ISSN":["1461-1570"],"issn-type":[{"value":"1461-1570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008]]}}}