{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T02:21:37Z","timestamp":1773368497120,"version":"3.50.1"},"reference-count":0,"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":[[1993,3]]},"abstract":"<jats:p> The relationship between covering spaces of graphs and subgroups of the free group leads to a rapid proof of the Nielsen-Schreier subgroup theorem. We show here that a similar relationship holds between immersions of graphs and closed inverse submonoids of free inverse monoids. We prove using these methods, that a closed inverse submonoid of a free inverse monoid is finitely generated if and only if it has finite index if and only if it is a rational subset of the free inverse monoid in the sense of formal language theory. We solve the word problem for the free inverse category over a graph \u0393. We show that immersions over \u0393 may be classified via conjugacy classes of loop monoids of the free inverse category over \u0393. In the case that \u0393 is a bouquet of X circles, we prove that the category of (connected) immersions over \u0393 is equivalent to the category of (transitive) representations of the free inverse monoid FIM(X). Such representations are coded by closed inverse submonoids of FIM(X). These monoids will be constructed in a natural way from groups acting freely on trees and they admit an idempotent pure retract onto a free inverse monoid. Applications to the classification of finitely generated subgroups of free groups via finite inverse monoids are developed. <\/jats:p>","DOI":"10.1142\/s021819679300007x","type":"journal-article","created":{"date-parts":[[2004,11,23]],"date-time":"2004-11-23T03:29:30Z","timestamp":1101180570000},"page":"79-99","source":"Crossref","is-referenced-by-count":47,"title":["FREE INVERSE MONOIDS AND GRAPH IMMERSIONS"],"prefix":"10.1142","volume":"03","author":[{"given":"STUART W.","family":"MARGOLIS","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, Center for Communication and Information Sciences, University of Nebraska-Lincoln Lincoln, NE 68588, U.S.A."}]},{"given":"JOHN C.","family":"MEAKIN","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Center for Communication and Information Sciences, University of Nebraska-Lincoln Lincoln, NE 68588, U.S.A."}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819679300007X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:20:58Z","timestamp":1565184058000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819679300007X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,3]]},"references-count":0,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1993,3]]}},"alternative-id":["10.1142\/S021819679300007X"],"URL":"https:\/\/doi.org\/10.1142\/s021819679300007x","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,3]]}}}