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|Paper IPM / M / 8293||
Let R be a commutative Noetherian ring, M a non-zero finitely
generated R-module and I an ideal of R. The purpose of this
paper is to develop the concept of Ratliff-Rush closure
~I(M) of I with respect to M. It is shown that the
sequence AssRR/~In(m), n−1,2,..., of
associated prime ideals is increasingly an eventually stabilizes.
This result extends Mirbagheri-Ratliff's main result in .
Furthermore, if R is local, then the operation I→~I(M) is a c*-operation on the set of ideals I
of R, each ideal I has a minimal Ratliff-Rush reduction J
with respect to M, and if K is an ideal between J and I,
then every minimal generating set for J extends to a minimal
generating set of K.
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