Rings graded by polycyclic-by-finite groups

William Chin; Declan P Quinn

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

Rings graded by polycyclic-by-finite groups

William Chin, Declan P Quinn

Research output: Contribution to journal › Article

17 Scopus citations

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 groupgraded rings. Our work extends several results on skew group rings, crossed products and group-graded rings.

Original language	English (US)
Pages (from-to)	235-241
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	102
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1988-0920979-3
State	Published - 1988
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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Chin, W., & Quinn, D. P. (1988). Rings graded by polycyclic-by-finite groups. Proceedings of the American Mathematical Society, 102(2), 235-241. https://doi.org/10.1090/S0002-9939-1988-0920979-3

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