Cancellation counterexamples in Krull dimension 1

Guralnick, Robert M.; Levy, Lawrence S.; Warfield, Robert B.

doi:10.1090/S0002-9939-1990-1009990-3

Cancellation counterexamples in Krull dimension $1$
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by Robert M. Guralnick, Lawrence S. Levy and Robert B. Warfield PDF

Proc. Amer. Math. Soc. 109 (1990), 323-326 Request permission

Abstract:

We show that direct-sum cancellation can fail for modules in a single genus, over commutative noetherian rings of dimension 1. The example provides an application of noncommutative methods (including "wild representation type") to commutative ring theory.

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