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Cancellation counterexamples in Krull dimension 1. (English) Zbl 0706.13010
Let $$\Lambda$$ be a module-finite algebra over a commutative ring R. We say that a $$\Lambda$$-module N is in the genus of M, if $$N_{{\mathfrak m}}\cong M_{{\mathfrak m}}$$ for each maximal ideal $${\mathfrak m}$$ of R. It is shown that direct-sum cancellation can fail for modules in a single genus over commutative noetherian rings of dimension 1. The example makes use of the notion of wild representation type to transfer a noncommutative example of Swan to the commutative situation.
Reviewer: S.Raianu

##### MSC:
 13C05 Structure, classification theorems for modules and ideals in commutative rings 16G60 Representation type (finite, tame, wild, etc.) of associative algebras
##### Keywords:
direct-sum cancellation; wild representation type
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