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Paper   IPM / M / 93
School of Mathematics
  Title:   Asymptotic attached prime ideals related to flat modules
1.  K. Divaani-Aazar
2.  M. Tousi
  Status:   Published
  Journal: Algebra Colloq.
  No.:  2
  Vol.:  6
  Year:  1999
  Pages:   193-204
  Supported by:  IPM
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(FR A) is determined. As a consequence, it is shown that the two sequences of attached prime ideals AttR(FRA′:FR A In) and AttR ((FR A′:FR A In)/(FRA": FR 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
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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