Krull-Schmidt fails for serial modules

Facchini, Alberto

doi:10.1090/S0002-9947-96-01740-0

Krull-Schmidt fails for serial modules
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by Alberto Facchini PDF

Trans. Amer. Math. Soc. 348 (1996), 4561-4575 Request permission

Abstract:

We answer a question posed by Warfield in 1975: the Krull-Schmidt Theorem does not hold for serial modules, as we show via an example. Nevertheless we prove a weak form of the Krull-Schmidt Theorem for serial modules (Theorem 1.9). And we show that the Grothendieck group of the class of serial modules of finite Goldie dimension over a fixed ring $R$ is a free abelian group.

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