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Solutions to two questions about the Weyl algebras


Author: V. Bavula
Journal: Proc. Amer. Math. Soc. 133 (2005), 1587-1591
MSC (2000): Primary 16S32, 16P40, 16W50, 16W70
Published electronically: December 6, 2004
MathSciNet review: 2120268
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Abstract: Affirmative answers are given to the following two questions about the Weyl algebras: a question of J. Alev: Does the first Weyl algebra contain a non-noetherian subalgebra?, and a question of T. Lenagan: Is there a uniserial module $M$ of length $2$ over the Weyl algebra $A_n$ with a holonomic submodule $U$ such that $V=M/U$ is non-holonomic?


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Additional Information

V. Bavula
Affiliation: Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, England
Email: v.bavula@sheffield.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07673-7
Received by editor(s): December 20, 2003
Received by editor(s) in revised form: February 13, 2004
Published electronically: December 6, 2004
Communicated by: Martin Lorenz
Article copyright: © Copyright 2004 American Mathematical Society