Krull-Schmidt fails for serial modules-Reference-Cited by-同舟云学术

Krull-Schmidt fails for serial modules

Published:1996 Issue:11 Volume:348 Page:4561-4575
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Facchini Alberto

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 R is a free abelian group.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1996-348-11/S0002-9947-96-01740-0/S0002-9947-96-01740-0.pdf

Reference8 articles.

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2. Krull-Schmidt fails for Artinian modules;Facchini, Alberto;Proc. Amer. Math. Soc.,1995

3. Uniserial modules: sums and isomorphisms of subquotients;Facchini, Alberto;Comm. Algebra,1990

4. Modules with semi-local endomorphism ring;Herbera, Dolors;Proc. Amer. Math. Soc.,1995

5. The lattice theory of ova;Ward, Morgan;Ann. of Math. (2),1939

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