Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On the global dimension of fixed rings

Author: Martin Lorenz
Journal: Proc. Amer. Math. Soc. 106 (1989), 923-932
MSC: Primary 16A72; Secondary 16A60
MathSciNet review: 972235
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be a finite group acting on a $ k$-algebra $ R$, and let $ S = {R^G}$ denote the fixed subring of $ R$. Our main interest is in the case where $ \left\vert G \right\vert$ is not invertible in $ R$. Instead, we assume that $ R$ is flat over $ S$ and that the trivial $ kG$-module $ k$ has a periodic projective resolution. (For a field $ k$ of characteristic $ p$, the latter condition holds precisely if the Sylow $ p$-subgroups of $ G$ are cyclic or generalized quaternion.) We use a periodicity result for Extgroups, established here in a more general setting that is independent of group actions, to estimate the global dimension of $ S$ in this case.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A72, 16A60

Retrieve articles in all journals with MSC: 16A72, 16A60

Additional Information

PII: S 0002-9939(1989)0972235-6
Article copyright: © Copyright 1989 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia