ASYMPTOTIC STABILITY OF Att_RTor₁^R((R/$Afr$ⁿ),A)

Abstract

Let R be a commutative ring. Let M respectively A denote a Noetherian respectively Artinian R-module, and a a finitely generated ideal of R. The main result of this note is that the sequence of sets (Att R Tor R 1 ((R/a n ), A)) n∈N is ultimately constant. As a consequence, whenever R is Noetherian, we show that Ass R Ext 1 R ((R/a 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.

On Finiteness Properties on Associated Primes of Local Cohomology Modules and Ext-Modules

“…In 2001, Khashyarmanesh and Salarian [7] proved that Ass R Ext 1 R (R/I n , M ) is independent of n for n >> 0. Afterwards, in [5], it was proved , for an integer…”