Please use this identifier to cite or link to this item: https://hdl.handle.net/10216/25719
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dc.creatorChristian Lomp
dc.date.accessioned2019-01-31T21:11:47Z-
dc.date.available2019-01-31T21:11:47Z-
dc.date.issued2008
dc.identifier.issn1306-6048
dc.identifier.othersigarra:48110
dc.identifier.urihttps://repositorio-aberto.up.pt/handle/10216/25719-
dc.descriptionGiven a finite group G acting as automorphisms on a ring A, the skew group ring A*G is an important tool for studying the structure of G-stable ideals of A. The ring A*G is G-graded, i.e. G coacts on A*G. The Cohen-Montgomery duality says that the smash product A*G#k[G]^* of A*Gwith the dual group ring k[G]^* is isomorphic to the full matrix ring M_n(A) over A, where n is the order of G. In this note we show how much of the Cohen-Montgomery duality carries over to partial group actions alpha in the sense of R.Exel. In particular we show that the smash product (A *_alpha G)#k[G]^* of the partial skew group ring A*_alpha G and k[G]^* is isomorphic to a direct product of the form K x eM_n(A)e where e is a certain idempotent of M_n(A) and K isa subalgebra of (A *_alpha G)#k[G]^*. Moreover A*_alpha G is shown to be isomorphic to a separable subalgebra of eM_n(A)e. We also look at duality for infinite partial group actions.
dc.description.abstractGiven a finite group G acting as automorphisms on a ring A, the skew group ring A*G is an important tool for studying the structure of G-stable ideals of A. The ring A*G is G-graded, i.e. G coacts on A*G. The Cohen-Montgomery duality says that the smash product A*G#k[G]^* of A*Gwith the dual group ring k[G]^* is isomorphic to the full matrix ring M_n(A) over A, where n is the order of G. In this note we show how much of the Cohen-Montgomery duality carries over to partial group actions alpha in the sense of R.Exel. In particular we show that the smash product (A *_alpha G)#k[G]^* of the partial skew group ring A*_alpha G and k[G]^* is isomorphic to a direct product of the form K x eM_n(A)e where e is a certain idempotent of M_n(A) and K isa subalgebra of (A *_alpha G)#k[G]^*. Moreover A*_alpha G is shown to be isomorphic to a separable subalgebra of eM_n(A)e. We also look at duality for infinite partial group actions.
dc.language.isoeng
dc.rightsopenAccess
dc.rights.urihttps://creativecommons.org/licenses/by-nc/4.0/
dc.subjectÁlgebra, Matemática
dc.subjectAlgebra, Mathematics
dc.titleDuality for partial group actions
dc.typeArtigo em Revista Científica Internacional
dc.contributor.uportoFaculdade de Ciências
dc.subject.fosCiências exactas e naturais::Matemática
dc.subject.fosNatural sciences::Mathematics
Appears in Collections:FCUP - Artigo em Revista Científica Internacional

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