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

Kemper, Ralf

doi:10.1090/S0002-9939-99-05098-4

Product-trace-rings and a question of G. S. Garfinkel
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Proc. Amer. Math. Soc. 128 (2000), 709-712 Request permission

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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