{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,7,4]],"date-time":"2022-07-04T05:51:17Z","timestamp":1656913877304},"reference-count":28,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1999,10]]},"abstract":"<jats:p> The main purpose of this paper is to investigate properties of an HNN extension of a semilattice, to give its equivalent characterizations and to discuss similarities with free groups. An HNN extension of a semilattice is shown to be a universal object in a certain category and an F-inverse cover over a free group for every inverse semigroup in the category. We also show that a graph with respect to a certain subset of an HNN extension of a semilattice is a tree and that this property characterizes an HNN extension of a semilattice. Moreover, we look into three subclasses: the class of full HNN extensions of semilattices with an identity, the class of universally E-unitary inverse semigroups and the class of HNN extensions of finite semilattices. The first class consists of factorizable E-unitary inverse semigroups whose maximal group homomorphic images are free. We obtain a generalization of the Nielsen\u2013Schreier subgroup theorem to this class. The second consists of inverse semigroups presented by relations on Dyck words. An inverse semigroup in the third class has a relatively easy finite presentation using a Dyck language and has solvable word problem. <\/jats:p>","DOI":"10.1142\/s0218196799000345","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T07:05:54Z","timestamp":1027753554000},"page":"555-596","source":"Crossref","is-referenced-by-count":8,"title":["HNN EXTENSIONS OF SEMILATTICES"],"prefix":"10.1142","volume":"09","author":[{"given":"AKIHIRO","family":"YAMAMURA","sequence":"first","affiliation":[{"name":"Communication System Division, Communications Research Laboratory, 4-2-1, Nukui-Kitamachi, Koganei, Tokyo\u00a0184-8795, Japan"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00969508"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196797000265"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02676602"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02194773"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573473"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1996.0206"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(75)90164-7"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-24.4.247"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/14.1.254"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500011251"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700041502"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1984-0728714-X"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1017\/S0017089500008442"},{"key":"p_19","first-page":"1","volume":"192","author":"McAlister D.","year":"1973","journal-title":"Trans. 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