{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T20:45:39Z","timestamp":1773261939507,"version":"3.50.1"},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2017,8,14]],"date-time":"2017-08-14T00:00:00Z","timestamp":1502668800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Aust. Math. Soc."],"published-print":{"date-parts":[[2018,6]]},"abstract":"Given a partial action $\\unicode[STIX]{x1D703}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> of a group on a set with an algebraic structure, we construct a reflector of $\\unicode[STIX]{x1D703}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> in the corresponding subcategory of global actions and study the question when this reflector is a globalization. In particular, if $\\unicode[STIX]{x1D703}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is a partial action on an algebra from a variety $\\mathsf{V}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, then we show that the problem reduces to the embeddability of a certain generalized amalgam of $\\mathsf{V}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-algebras associated with $\\unicode[STIX]{x1D703}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. As an application, we describe globalizable partial actions on semigroups, whose domains are ideals.<\/jats:p>","DOI":"10.1017\/s1446788717000167","type":"journal-article","created":{"date-parts":[[2017,8,14]],"date-time":"2017-08-14T06:41:04Z","timestamp":1502692864000},"page":"358-379","source":"Crossref","is-referenced-by-count":9,"title":["REFLECTORS AND GLOBALIZATIONS OF PARTIAL ACTIONS OF GROUPS"],"prefix":"10.1017","volume":"104","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4504-3261","authenticated-orcid":false,"given":"MYKOLA","family":"KHRYPCHENKO","sequence":"first","affiliation":[]},{"given":"BORIS","family":"NOVIKOV","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2017,8,14]]},"reference":[{"key":"S1446788717000167_r15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65374-2"},{"key":"S1446788717000167_r6","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-04-03519-6"},{"key":"S1446788717000167_r17","doi-asserted-by":"publisher","DOI":"10.2307\/2372346"},{"key":"S1446788717000167_r14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9839-7"},{"key":"S1446788717000167_r21","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-3.1.243"},{"key":"S1446788717000167_r5","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-06-08503-0"},{"key":"S1446788717000167_r13","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-3483-7"},{"key":"S1446788717000167_r18","doi-asserted-by":"publisher","DOI":"10.2307\/2372282"},{"key":"S1446788717000167_r2","volume-title":"Automata and Algebras in Categories","author":"Ad\u00e1mek","year":"1990"},{"key":"S1446788717000167_r3","volume-title":"The Algebraic Theory of Semigroups","author":"Clifford","year":"1961"},{"key":"S1446788717000167_r4","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-8399-1"},{"key":"S1446788717000167_r9","doi-asserted-by":"publisher","DOI":"10.1201\/9781420010961.ch14"},{"key":"S1446788717000167_r11","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1112\/jlms\/2.Part_3.389","article-title":"Free products of semigroups amalgamating an ideal","volume":"2","author":"Grillet","year":"1970","journal-title":"J. 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