Johnson, Francis;
(2024)
A cancellation theorem for metacyclic group rings.
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
10.1007/s13366-024-00772-9.
(In press).
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Abstract
A ring has stably free cancellation when every stably free -module is free. Let G = Cp Cq be a finite metacyclic group where p is an odd prime and q is a positive integral divisor of p − 1. We show that the group ring R[G] has stably free cancellation when R = Z[t1, t −1 1 ,... tm, t−1 m , x1,... xn] is a ring of mixed polynomials and Laurent polynomials over the integers. As a consequence, when C(m) ∞ is the free abelian group of rank m then the integral group ring Z[G(p, q) × C(m) ∞ ] has stably free cancellation.
| Type: | Article |
|---|---|
| Title: | A cancellation theorem for metacyclic group rings |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s13366-024-00772-9 |
| Publisher version: | https://doi.org/10.1007/s13366-024-00772-9 |
| Language: | English |
| Additional information: | Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Stably free module · Locally free module · Milnor square |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10198327 |
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