On the Annihilation of local homology modules

Research

Title	On the Annihilation of local homology modules
Type	JournalPaper
Keywords	Annihilator of local homology modules_local homology modules
Year	2012
Journal	Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
DOI
Researchers	Amir Mafi

Let a b be two ideals of commutative Noetherian ring R and A an

Artinian R-module. For a non-negative integer n, we show that

up+q=n Ann(TorR

p (R=b;Ha

q (A))) Ann(TorR

n (R=b;A)):

As an immediate consequence, if Ha

i (A) is Artinian for all i < n then a

Rad(Ann(Hb

i (A))) for all i < n. Moreover, we prove that if a = (x1; : : : ; xn)

and c = \t1\n

i=0 Ann(TorR

i (R=at;A)), then ck \n􀀀1

i=0 Ann(Ha

i (A)) where

k = (n

2 ]).