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`https://hdl.handle.net/10216/25719`

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DC Field | Value | Language |
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dc.creator | Christian Lomp | |

dc.date.accessioned | 2019-01-31T21:11:47Z | - |

dc.date.available | 2019-01-31T21:11:47Z | - |

dc.date.issued | 2008 | |

dc.identifier.issn | 1306-6048 | |

dc.identifier.other | sigarra:48110 | |

dc.identifier.uri | https://repositorio-aberto.up.pt/handle/10216/25719 | - |

dc.description | Given 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.abstract | Given 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.iso | eng | |

dc.rights | openAccess | |

dc.rights.uri | https://creativecommons.org/licenses/by-nc/4.0/ | |

dc.subject | Álgebra, Matemática | |

dc.subject | Algebra, Mathematics | |

dc.title | Duality for partial group actions | |

dc.type | Artigo em Revista Científica Internacional | |

dc.contributor.uporto | Faculdade de Ciências | |

dc.subject.fos | Ciências exactas e naturais::Matemática | |

dc.subject.fos | Natural sciences::Mathematics | |

Appears in Collections: | FCUP - Artigo em Revista Científica Internacional |

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