Rings graded by polycyclic-by-finite groups

William Chin, Declan P Quinn

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)235-241
Number of pages7
JournalProceedings of the American Mathematical Society
Volume102
Issue number2
DOIs
StatePublished - 1988
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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