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Paper IPM / M / 498  


Abstract:  
Let R be a commutative ring. Let M respectively A denote a
Noetherian respectively Artinian Rmodule, and \fraka a
finitely generated ideal of R. The main result of this note is
that the sequence of sets (Att_{R}Tor^{R}_{1}((R/\fraka^{n}),A))_{n ∈ \mathbbN} is
ultimately constant. As a consequence, whenever R is Noetherian,
we show that Ass_{R} Ext^{1}_{R}((R/\fraka^{n}),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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