“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 93
School of Mathematics
  Title:   Asymptotic attached prime ideals related to flat modules
  Author(s): 
1.  K. Divaani-Aazar
2.  M. Tousi
  Status:   Published
  Journal: Algebra Colloq.
  No.:  2
  Vol.:  6
  Year:  1999
  Pages:   193-204
  Supported by:  IPM
  Abstract:
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
AttR((HomR(F,A′):HomR(F,A)In)/(HomR(F,A"):HomR(F,A)In)).
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.

Download TeX format
back to top
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
scroll left or right