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Prüfer domains and pure submodules of direct sums of ideals

Part of: Arithmetic rings and other special rings

Published online by Cambridge University Press:  26 February 2010

Bruce Olberding
Bruce Olberding
Affiliation:
Department of Mathematics, University of Louisiana at Monroe, Monroe, LA 71209, U.S.A. E-mail: maolberding@alpha.nlu.edu
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Abstract

It is shown that an integral domain R has the property that every pure submodule of a finite direct sum of ideals of R is a summand if and only if R is an h-local Prüfer domain; equivalently, (J + K:I) = (J:I) + (K:I) for all ideals I, J and K of R. These results are extended to submodules of the quotient field of an integral domain.

MSC classification

Secondary: 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations
Type
Research Article
Information
Mathematika , Volume 46 , Issue 2 , December 1999 , pp. 425 - 432
Copyright
Copyright © University College London 1999

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