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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Decomposability of finitely presented modules


Author: R. B. Warfield
Journal: Proc. Amer. Math. Soc. 25 (1970), 167-172
MSC: Primary 13.40
MathSciNet review: 0254030
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Abstract: It is proved that a commutative ring with $ 1$ has the property that every finitely presented module is a summand of a direct sum of cyclic modules if and only if it is locally a generalized valuation ring. A Noetherian ring has this property if and only if it is a direct product of a finite number of Dedekind domains and an Artinian principal ideal ring. Any commutative local ring which is not a generalized valuation ring has finitely presented indecomposable modules requiring arbitrarily large numbers of generators.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0254030-4
PII: S 0002-9939(1970)0254030-4
Keywords: Indecomposable modules, generalized valuation rings, direct sums of cyclic modules
Article copyright: © Copyright 1970 American Mathematical Society