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) |
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Pages (from-to) | 235-241 |
Number of pages | 7 |
Journal | Proceedings of the American Mathematical Society |
Volume | 102 |
Issue number | 2 |
DOIs | |
State | Published - Feb 1988 |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics