{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T23:10:11Z","timestamp":1712358611939},"reference-count":24,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01n02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2011,2]]},"abstract":"<jats:p>We prove that a finitely presented Rees quotient of a free inverse semigroup has polynomial growth if and only if it has bounded height. This occurs if and only if the set of nonzero reduced words has bounded Shirshov height and all nonzero reduced but not cyclically reduced words are nilpotent. This occurs also if and only if the set of nonzero geodesic words have bounded Shirshov height. We also give a simple sufficient graphical condition for polynomial growth, which is necessary when all zero relators are reduced. As a final application of our results, we give an inverse semigroup analogue of a classical result that characterizes polynomial growth of finitely presented Rees quotients of free semigroups in terms of connections between non-nilpotent elements and primitive words that label loops of the Ufnarovsky graph of the presentation.<\/jats:p>","DOI":"10.1142\/s0218196711006182","type":"journal-article","created":{"date-parts":[[2011,4,6]],"date-time":"2011-04-06T12:14:25Z","timestamp":1302092065000},"page":"315-328","source":"Crossref","is-referenced-by-count":3,"title":["GROWTH OF FINITELY PRESENTED REES QUOTIENTS OF FREE INVERSE SEMIGROUPS"],"prefix":"10.1142","volume":"21","author":[{"given":"L. M.","family":"SHNEERSON","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Hunter College, The City University of New York, 695 Park Avenue, New York, NY 10065, USA"}]},{"given":"D.","family":"EASDOWN","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"603","volume":"25","author":"Bass H.","journal-title":"Proc. London Math. Soc."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1962-10745-9"},{"key":"rf3","series-title":"Math. Surveys","volume-title":"The Algebraic Theory of Semigroups","author":"Clifford A. 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