{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,7]],"date-time":"2024-07-07T11:12:04Z","timestamp":1720350724582},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2002,12]]},"abstract":" We show how the Rhodes expansion \u015c of any stable semigroup S embeds into the cascade integral (a natural generalization of the wreath product) of permutation-reset transformation semigroups with zero adjoined. The permutation groups involved are exactly the Sch\u00fctzenberger groups of the [Formula: see text]-classes of S. Since S \u2190\u2190 \u015c is an aperiodic map via which all subgroups of S lift to \u015c, this results in a strong Krohn\u2013Rhodes\u2013Zeiger decomposition for the entire class of stable semigroups. This class includes all semigroups that are finite, torsion, finite [Formula: see text]-above, compact Hausdorff, or relatively free profinite, as well as many other semigroups. Even if S is not stable, one can expand it using Henckell's expansion and then apply our embedding. This gives a simplified proof of the Holonomy Embedding theorem for all semigroups. <\/jats:p>","DOI":"10.1142\/s0218196702001206","type":"journal-article","created":{"date-parts":[[2002,12,20]],"date-time":"2002-12-20T11:13:16Z","timestamp":1040382796000},"page":"791-810","source":"Crossref","is-referenced-by-count":3,"title":["HOLONOMY EMBEDDING OF ARBITRARY STABLE SEMIGROUPS"],"prefix":"10.1142","volume":"12","author":[{"given":"GILLIAN Z.","family":"ELSTON","sequence":"first","affiliation":[{"name":"Department of Mathematics, Hofstra University, Hempstead NY 11549-1030, USA"}]},{"given":"CHRYSTOPHER L.","family":"NEHANIV","sequence":"additional","affiliation":[{"name":"Faculty of Engineering & Information Sciences, University of Hertfordshire, Hatfield Herts AL10 9AB, UK"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(94)00063-O"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(84)90092-6"},{"key":"p_5","first-page":"86","volume":"55","author":"Henckell K.","year":"1988","journal-title":"J. Pure Appl. Algebra"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(88)90043-6"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500018163"},{"key":"p_9","first-page":"5","volume":"1","author":"Krohn K.","year":"1968","journal-title":"Chaps."},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196795000100"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196791000171"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(67)90228-8"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196702001206","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:56:34Z","timestamp":1565128594000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196702001206"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,12]]},"references-count":9,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2002,12]]}},"alternative-id":["10.1142\/S0218196702001206"],"URL":"https:\/\/doi.org\/10.1142\/s0218196702001206","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,12]]}}}