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Simplicity of noncommutative Dedekind domains

Authors: K. R. Goodearl and J. T. Stafford
Journal: Proc. Amer. Math. Soc. 133 (2005), 681-686
MSC (2000): Primary 16P40, 16E60
Published electronically: August 24, 2004
MathSciNet review: 2113915
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Abstract: The following dichotomy is established: A finitely generated, complex Dedekind domain that is not commutative is a simple ring. Weaker versions of this dichotomy are proved for Dedekind prime rings and hereditary noetherian prime rings.

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Additional Information

K. R. Goodearl
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106-3080

J. T. Stafford
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109

Keywords: Dedekind domain, simple ring, invertible ideal, HNP ring
Received by editor(s): November 6, 2003
Published electronically: August 24, 2004
Additional Notes: The research of both authors was partially supported by grants from the National Science Foundation. Some of it was carried out while the authors participated in the Noncommutative Algebra Year (1999-2000) at the Mathematical Sciences Research Institute in Berkeley, and they thank MSRI for its support
Communicated by: Lance W. Small
Article copyright: © Copyright 2004 American Mathematical Society

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