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Partial Skew Group Rings Over Polycyclic by Finite Groups

Title
Partial Skew Group Rings Over Polycyclic by Finite Groups
Type
Article in International Scientific Journal
Year
2011
Authors
Paula A.A.B. Carvalho
(Author)
FCUP
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Wagner Cortes
(Author)
Other
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Miguel Ferrero
(Author)
Other
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Journal
Vol. 14 No. 3
Pages: 449-462
ISSN: 1386-923X
Publisher: Springer Nature
Indexing
Scientific classification
FOS: Natural sciences > Mathematics
CORDIS: Physical sciences > Mathematics > Algebra
Other information
Authenticus ID: P-002-RAY
Resumo (PT): In this paper we consider a partial action α of a polycyclic by finite group G on a ring R. We prove that if R is right noetherian, then the partial skew group ring R ⋆  α G is also right noetherian. Extending the methods of Passman in Passman (Trans Am Math Soc 301:737–759, 1987), we obtain a description of the prime spectrum of R ⋆  α G. The results obtained are applied to get bounds for the Krull dimension and the classical Krull dimension of R ⋆  α G.
Abstract (EN): In this paper we consider a partial action alpha of a polycyclic by finite group G on a ring R. We prove that if R is right noetherian, then the partial skew group ring R(*alpha) G is also right noetherian. Extending the methods of Passman in Passman (Trans Am Math Soc 301:737-759, 1987), we obtain a description of the prime spectrum of R R(*alpha) G. The results obtained are applied to get bounds for the Krull dimension and the classical Krull dimension of R (*alpha) G.
Language: English
Type (Professor's evaluation): Scientific
Contact: pbcarval@fc.up.pt; cortes@mat.ufrgs.br; mferrero@mat.ufrgs.br
No. of pages: 14
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