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IPM
30
YEARS OLD

“School of Mathematics”

Paper   IPM / M / 498
   School of Mathematics
  Title: Asymptotic stability of AttR Tor1R((R/\frakan),A)
  Author(s):
1 . K. Khashyarmanesh
2 . Sh. Salarian
  Status: Published
  Journal: Proc. Edinburgh Math. Soc.
  Vol.: 44
  Year: 2001
  Pages: 479-483
  Supported by: IPM
  Abstract:
Let R be a commutative ring. Let M respectively A denote a Noetherian respectively Artinian R-module, and \fraka a finitely generated ideal of R. The main result of this note is that the sequence of sets (AttRTorR1((R/\frakan),A))n ∈ \mathbbN is ultimately constant. As a consequence, whenever R is Noetherian, we show that AssR Ext1R((R/\frakan),M) is ultimately constant for large n, which is an affirmative answer to the question that was posed by Melkersson and Schenzel in the case i=1.

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