Abstract
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.
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The first named author was supported by Grices, Portugal, and Centro de Matemática da Universidade do Porto (CMUP), financed by FCT through the programes POCTI and POSI. The third named author was partially supported by CNPq and Capes, Brazil. This paper was written as a consequence of a project of cooperation between Capes and Grices.
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Carvalho, P.A.A.B., Cortes, W. & Ferrero, M. Partial Skew Group Rings Over Polycyclic by Finite Groups. Algebr Represent Theor 14, 449–462 (2011). https://doi.org/10.1007/s10468-009-9197-7
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DOI: https://doi.org/10.1007/s10468-009-9197-7