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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Product-trace-rings
and a question of G. S. Garfinkel


Author: Ralf Kemper
Journal: Proc. Amer. Math. Soc. 128 (2000), 709-712
MSC (1991): Primary 12J25, 13A18, 13C13, 13E05, 13F30, 13J10, 46N05
Published electronically: July 28, 1999
MathSciNet review: 1636970
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Abstract: It is an open question as to whether every left coherent ring $R$ satisfying the intersection property for finitely generated left ideals of $R$ is a right-product-trace-ring or not. $R$ is a right-product-trace-ring iff every product of trace-right-$R$-modules (= universally torsionless-right-$R$-modules) is a trace-right-$R$-module. This question is shown to have a negative answer. Furthermore, looking at all valuation domains, the complete product-trace-rings, the product-trace-rings and the product-content-rings are characterized.


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Additional Information

Ralf Kemper
Affiliation: Fernuniversität, Fachbereich Mathematik, D 58084 Hagen, Germany

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05098-4
PII: S 0002-9939(99)05098-4
Keywords: Trace-module, universally torsionless module, product-trace-ring, ((maximally) complete) valuation domain, spherically complete field, content-module, content-ideal
Received by editor(s): November 25, 1997
Received by editor(s) in revised form: May 1, 1998
Published electronically: July 28, 1999
Dedicated: Dedicated to H. Röhrl on the occasion of his 70th birthday
Communicated by: Ken Goodearl
Article copyright: © Copyright 1999 American Mathematical Society