Abstract:
Prime Goldie rings graded by group are studied. It is proved that there exists a completely gr-reducible graded ring of fractions in the case of a grading group with a finite commutator subgroup (enhancing results of Goodearl–Stafford obtained for Abelian groups), and an example for which such a ring doesn't exist is constructed (a counterexample for a semi-prime ring was already known).
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