Group actions of prime order on local normal rings

Kiràly, Franz; Lütkebohmert, Werner

doi:10.2140/ant.2013.7.63

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

Group actions of prime order on local normal rings

Franz Kiràly and Werner Lütkebohmert

Vol. 7 (2013), No. 1, 63–74

DOI: 10.2140/ant.2013.7.63

Abstract

Let $B$ be a Noetherian normal local ring and $G \subset Aut (B)$ be a cyclic group of local automorphisms of prime order. Let $A$ be the subring of $G$ -invariants of $B$ and assume that $A$ is Noetherian. We prove that $B$ is a monogenous $A$ -algebra if and only if the augmentation ideal of $B$ is principal. If in particular $B$ is regular, we prove that $A$ is regular if the augmentation ideal of $B$ is principal.

Keywords

algebraic geometry, commutative algebra, group actions

Mathematical Subject Classification 2010

Primary: 14L30

Secondary: 13A50

Milestones

Received: 14 April 2011

Revised: 23 January 2012

Accepted: 20 February 2012

Published: 28 March 2013

Authors

Franz Kiràly
Berlin Institute of Technology Machine Learning Group Marchstraße 23 10587 Berlin Germany	Freie Universität Berlin Discrete Geometry Group Arnimallee 2 14195 Berlin Germany	Mathematisches Forschungsinstitut Oberwolfach Schwarzwaldstraße 9-11 77709 Oberwolfach Germany

Werner Lütkebohmert
Dept. of Pure Mathematics University of Ulm Helmholtzstraße 18 89069 Ulm Germany

Vol. 7, No. 1, 2013