Partial Skew Polynomial Rings and Goldie Rings

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.

Key Words:

• Goldie rings
• Partial action
• Semiprime rings

2000 Mathematics Subject Classification:

• Primary 16S36
• Secondary 16P60

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.