{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T07:53:30Z","timestamp":1655193210397},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asian-European J. Math."],"published-print":{"date-parts":[[2013,3]]},"abstract":"<jats:p> If X and Y are sets, we let P(X, Y) denote the set of all partial transformations from X into Y (that is, all mappings whose domain and range are subsets of X and Y, respectively). If \u03b8 \u2208 P(Y, X), then P(X, Y) is a so-called \"generalized semigroup\" of transformations under the \"sandwich operation\": \u03b1 * \u03b2 = \u03b1 \u25e6 \u03b8 \u25e6 \u03b2, for each \u03b1, \u03b2 \u2208 P(X, Y). We denote this semigroup by P(X, Y, \u03b8) and, in this paper, we characterize Green's relations on it: that is, we study equivalence relations which determine when principal left (or right, or 2-sided) ideals in P(X, Y, \u03b8) are equal. This solves a problem raised by Magill and Subbiah in 1975. We also discuss the same idea for important subsemigroups of P(X, Y, \u03b8) and characterize when these semigroups satisfy certain regularity conditions. <\/jats:p>","DOI":"10.1142\/s179355711350006x","type":"journal-article","created":{"date-parts":[[2013,4,25]],"date-time":"2013-04-25T01:51:27Z","timestamp":1366854687000},"page":"1350006","source":"Crossref","is-referenced-by-count":3,"title":["REGULAR ELEMENTS AND GREEN'S RELATIONS IN GENERALIZED TRANSFORMATION SEMIGROUPS"],"prefix":"10.1142","volume":"06","author":[{"given":"Suzana","family":"Mendes-Gon\u00e7alves","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica, Universidade do Minho, 4710 Braga, Portugal"}]},{"given":"R. P.","family":"Sullivan","sequence":"additional","affiliation":[{"name":"School of Mathematics &amp; Statistics, University of Western Australia, Nedlands, 6009, Australia"}]}],"member":"219","published-online":{"date-parts":[[2013,4,24]]},"reference":[{"key":"rf1","first-page":"581","volume":"2","author":"Chanmuang P.","journal-title":"Int. J. Algebra"},{"key":"rf2","first-page":"161","volume":"45","author":"Chinram R.","journal-title":"Kyungpook Math. J."},{"key":"rf3","first-page":"513","volume":"30","author":"Chinram R.","journal-title":"Far East J. Math. Sci."},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S1793557108000266"},{"key":"rf5","series-title":"Mathematical Surveys","volume-title":"The Algebraic Theory of Semigroups","volume":"2","author":"Clifford A. H.","year":"1961"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02572687"},{"key":"rf7","first-page":"209","volume":"27","author":"Ehrlich G.","journal-title":"Port. Math."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-200066151"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(01)00076-7"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700005115"},{"key":"rf11","first-page":"194","volume":"31","author":"Magill K. D.","journal-title":"Proc. London Math. Soc."},{"key":"rf13","series-title":"Canadian Mathematics Society Advanced Texts","volume-title":"Completely Regular Semigroups","volume":"23","author":"Petrich M.","year":"1999"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573653"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700034492"},{"key":"rf17","first-page":"59","volume":"21","author":"Sullivan R. P.","journal-title":"Pure Math. Appl."},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1142\/S1005386707000387"}],"container-title":["Asian-European Journal of Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S179355711350006X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:54:41Z","timestamp":1565114081000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S179355711350006X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3]]},"references-count":16,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2013,4,24]]},"published-print":{"date-parts":[[2013,3]]}},"alternative-id":["10.1142\/S179355711350006X"],"URL":"https:\/\/doi.org\/10.1142\/s179355711350006x","relation":{},"ISSN":["1793-5571","1793-7183"],"issn-type":[{"value":"1793-5571","type":"print"},{"value":"1793-7183","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,3]]}}}