Abstract
We prove that if R is a semiprime ring and α is a partial action of an infinite cyclic group on R, then R is right Goldie if and only if R[x; α] is right Goldie if and only if R⟨x; α⟩ is right Goldie, where R[x; α] (R⟨x; α⟩) denotes the partial skew (Laurent) polynomial ring over R. In addition, R⟨x; α⟩ is semiprime while R[x; α] is not necessarily semiprime.
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ACKNOWLEDGMENTS
Ferrero was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, Brazil). Marubayashi was supported by JSPS (Japan) and ABC (Brazil).
Notes
Communicated by E. R. Puczylowski.