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Prüfer domains and pure submodules of direct sums of ideals
Author(s) -
Olberding Bruce
Publication year - 1999
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300007889
Subject(s) - mathematics , integral domain , quotient , domain (mathematical analysis) , pure mathematics , field (mathematics) , property (philosophy) , ideal (ethics) , discrete mathematics , mathematical analysis , law , philosophy , epistemology , political science
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.