Partial Skew Group Rings Over Polycyclic by Finite Groups

• Type: Article in International Scientific Journal
• Date: 2011

Authors

Paula A.A.B. Carvalho (Author) FCUP; Wagner Cortes (Author) Other; Miguel Ferrero (Author) Other

Journal

Title: Algebras and Representation Theory

Vol. 14 No. 3

Pages: 449-462

ISSN: 1386-923X

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 7 Citations

ISI Web of Science

Scopus - 10 Citations

Scientific classification

FOS: Natural sciences > Mathematics

CORDIS: Physical sciences > Mathematics > Algebra

Other information

Authenticus ID: P-002-RAY

DOI: 10.1007/s10468-009-9197-7

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

No. of pages: 14