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dc.contributor.advisorSant'Ana, Alveri Alvespt_BR
dc.contributor.authorCastro, Felipe Lopespt_BR
dc.date.accessioned2020-03-06T04:14:05Zpt_BR
dc.date.issued2015pt_BR
dc.identifier.urihttp://hdl.handle.net/10183/206505pt_BR
dc.description.abstractPartial module coalgebra and partial comodule coalgebra are the dual notions of partial module algebra, and all these structures are close related. Partial module algebra was defined by Caenepeel and Janssen in [11] and developed in a certain direction by Alves and Batista in [1–3]. We are interested in some constructions made by Alves and Batista, namely: globalization for partial module algebras, a Morita context relating the invariant subalgebra and the partial smash product, and Galois theory. In this work, we introduce the notion of globalization for partial module coalgebra and for partial comodule coalgebra. We show that every partial module coalgebra is globalizable constructing a globalization, named standard. For the case of partial comodule coalgebra we need assume some kind of rationality condition to obtain a correspondent globalization. Moreover, for a partial comodule coalgebra, we construct a Morita-Takeuchi context relating the coinvariant coalgebra and the partial smash coproduct, and we define a Galois coextension and show some properties, relating the Galois coextension for partial comodule coalgebra with the Galois extension for partial coaction on algebras, extending results of Dascalescu, Raianu, and Zhang obtained in [20].en
dc.format.mimetypeapplication/pdfpt_BR
dc.language.isoengpt_BR
dc.rightsOpen Accessen
dc.subjectHopf algebrasen
dc.subjectÁlgebrapt_BR
dc.subjectTeoria de galoispt_BR
dc.subjectPartial actionen
dc.subjectPartial coactionen
dc.subjectGlobalizationen
dc.subjectGalois theoryen
dc.titleOn partial (Co)actions on coalgebras : globalizations and some galois theorypt_BR
dc.typeTesept_BR
dc.identifier.nrb000955722pt_BR
dc.degree.grantorUniversidade Federal do Rio Grande do Sulpt_BR
dc.degree.departmentInstituto de Matemáticapt_BR
dc.degree.programPrograma de Pós-Graduação em Matemáticapt_BR
dc.degree.localPorto Alegre, BR-RSpt_BR
dc.degree.date2015pt_BR
dc.degree.leveldoutoradopt_BR


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