{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:41:59Z","timestamp":1740134519872,"version":"3.37.3"},"reference-count":5,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Oficina de Investigaciones y Desarrollo Cient\u00edfico de la Universidad del Tolima"},{"DOI":"10.13039\/501100004263","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado do Rio Grande do Sul","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004263","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We consider a partial action<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>X<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03b1<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:math>with enveloping action<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>T<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03b2<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:math>. In this work we extend<jats:italic>\u03b1<\/jats:italic>to a partial action on the ring<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>P<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>X<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><mml:mo>,<\/mml:mo><mml:mi mathvariant=\"normal\">\u0394<\/mml:mi><mml:mo>,<\/mml:mo><mml:mo>\u2229<\/mml:mo><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:math>and find its enveloping action<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>E<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03b2<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:math>. Finally, we introduce the concept of partial action of<jats:italic>finite type<\/jats:italic>to investigate the relationship between<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>E<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03b2<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>P<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>T<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><mml:mo>,<\/mml:mo><mml:mi>\u03b2<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:math>.<\/jats:p>","DOI":"10.1155\/2013\/376915","type":"journal-article","created":{"date-parts":[[2013,2,4]],"date-time":"2013-02-04T16:03:03Z","timestamp":1359993783000},"page":"1-4","source":"Crossref","is-referenced-by-count":1,"title":["Partial Actions and Power Sets"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8713-2449","authenticated-orcid":true,"given":"Jes\u00fas","family":"\u00c1vila","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas y Estad\u00edstica, Universidad del Tolima, Ibagu\u00e9, Colombia"}]},{"given":"Jo\u00e3o","family":"Lazzarin","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade Federal de Santa Maria, Santa Maria, RS, Brazil"}]}],"member":"311","reference":[{"key":"4","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-98-04575-4"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-1236(02)00032-0"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-04-03519-6"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1080\/00927870903023139"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2007.12.009"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/376915.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/376915.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/376915.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,18]],"date-time":"2016-08-18T14:22:43Z","timestamp":1471530163000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2013\/376915\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":5,"alternative-id":["376915","376915"],"URL":"https:\/\/doi.org\/10.1155\/2013\/376915","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2013]]}}}