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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机译：在本文中，我们考虑了环R上有限基团G对多环的局部作用α。我们证明，如果R是正确的noetherian，则偏偏环环R⋆α G也是正确的Noetherian。扩展了Passman中Passman的方法（Trans Am Math Soc 301：737–759，1987），我们获得了R⋆α G的素谱的描述。所得结果用于求界R⋆α G的Krull维数和经典Krull维数。
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