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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
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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Article copyright: © Copyright 1988 American Mathematical Society

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