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“School of Mathematics”

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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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