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Algebras in which every subalgebra is noetherian


Authors: D. Rogalski, S. J. Sierra and J. T. Stafford
Journal: Proc. Amer. Math. Soc. 142 (2014), 2983-2990
MSC (2010): Primary 16P40, 16S38, 16W50, 16W70
Published electronically: May 21, 2014
MathSciNet review: 3223353
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Abstract: We show that the twisted homogeneous coordinate rings of elliptic curves by infinite order automorphisms have the curious property that every subalgebra is both finitely generated and noetherian. As a consequence, we show that a localisation of a generic Skylanin algebra has the same property.


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Additional Information

D. Rogalski
Affiliation: Department of Mathematics, University of California, San Diego, La Jolla, California 92093-0112
Email: drogalsk@math.ucsd.edu

S. J. Sierra
Affiliation: School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland
Email: s.sierra@ed.ac.uk

J. T. Stafford
Affiliation: School of Mathematics, University of Manchester, Manchester M13 9PL, England
Email: Toby.Stafford@manchester.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-12052-1
Keywords: Noetherian ring, twisted homogeneous coordinate ring, Sklyanin algebra, supernoetherian ring
Received by editor(s): January 24, 2012
Received by editor(s) in revised form: September 24, 2012
Published electronically: May 21, 2014
Additional Notes: The first author was partially supported by NSF grant DMS-0900981.
The second author was supported by an NSF Postdoctoral Research Fellowship, grant DMS-0802935.
The third author is a Royal Society Wolfson Research Merit Award holder.
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2014 American Mathematical Society