Let I be an ideal of the commutative ring R and F a flat
R-module. Let A denote an Artinian R-module and
A" ⊆ A′ submodules of A. In this paper, the set
AttR(F⊗R A) is determined. As a consequence, it
is shown that the two sequences of attached prime ideals
AttR(F⊗RA′:F⊗R A In) and
AttR ((F⊗R A′:F⊗R A In)/(F⊗RA": F⊗R A In)) eventually become constant for large
n. Also, the same result is shown to be true for the two
sequences
AttR(HomR(F,A′):HomR(F,A)In)
and
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AttR((HomR(F,A′):HomR(F,A)In)/(HomR(F,A"):HomR(F,A)In)). |
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Moreover, in the case where R is Noetherian, the set
AttR (HomR(F,A)) is determined and a
criterion for the non-vanishing of certain local cohomology
modules is given.
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