Rings graded by polycyclic-by-finite groups-Reference-Cited by-同舟云学术

Rings graded by polycyclic-by-finite groups

Published:1988 Issue:2 Volume:102 Page:235-241
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Chin William,Quinn Declan

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1988-102-02/S0002-9939-1988-0920979-3/S0002-9939-1988-0920979-3.pdf

Reference12 articles.

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3. G. Bergman, Homogeneous elements and prime ideals in 𝐙-graded rings, preprint.

4. A duality theorem for Hopf module algebras;Blattner, Robert J.;J. Algebra,1985

5. Prime ideals in differential operator rings and crossed products of infinite groups;Chin, William;J. Algebra,1987

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