Vol. 7, No. 1, 2013

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Group actions of prime order on local normal rings

Franz Kiràly and Werner Lütkebohmert

Vol. 7 (2013), No. 1, 63–74
Abstract

Let B be a Noetherian normal local ring and G 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