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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.