Rings graded by polycyclic-by-finite groups

Authors:
William Chin and Declan Quinn

Journal:
Proc. Amer. Math. Soc. **102** (1988), 235-241

MSC:
Primary 16A03,; Secondary 16A27,16A33,16A55

DOI:
https://doi.org/10.1090/S0002-9939-1988-0920979-3

MathSciNet review:
920979

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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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0920979-3

Article copyright:
© Copyright 1988
American Mathematical Society