Rings graded by polycyclic-by-finite groups

Chin, William; Quinn, Declan

doi:10.1090/S0002-9939-1988-0920979-3

Rings graded by polycyclic-by-finite groups
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by William Chin and Declan Quinn PDF

Proc. Amer. Math. Soc. 102 (1988), 235-241 Request permission

Abstract:

We use the duality between group gradings and group actions to study polycyclic-by-finite group-graded rings. We show that, for such rings, graded Noetherian implies Noetherian and relate the graded Krull dimension to the Krull dimension. In addition we find a bound on the length of chains of prime ideals not containing homogeneous elements when the grading group is nilpotent-by-finite. These results have suitable corollaries for strongly group-graded rings. Our work extends several results on skew group rings, crossed products and group-graded rings.

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