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

DOI:
https://doi.org/10.1090/S0002-9939-04-07574-4

Published electronically:
August 24, 2004

MathSciNet review:
2113915

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

Email:
goodearl@math.ucsb.edu

**J. T. Stafford**

Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109

Email:
jts@umich.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07574-4

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