LAUSR

Let $$(R,\mathfrak {m})$$(R,m) be a Noetherian local ring, I be an ideal of R, and M be a finitely generated R-module such that $${\text {H}}_I^t(M)$$HIt(M) is Artinian and I-cofinite, where $$t={\text {cd}}\,(I,M)$$t=cd(I,M). In this paper, we give some equivalent conditions for the property $$\begin{aligned} {\text {Ann}}\,_R\left( 0:_{{\text {H}}_I^t (M)} \mathfrak {p}\right) =\mathfrak {p}~\text {for all prime ideals }~ \mathfrak {p}\supseteq {\text {Ann}}\,_R{\text {H}}_I^t(M).(*) \end{aligned}$$AnnR0:HIt(M)p=pfor all prime idealsp⊇AnnRHIt(M).(∗)Also, we show that if $${\text {H}}_I^t(M)$$HIt(M) satisfies the property $$(*)$$(∗), then $${\text {H}}_I^t(M)\cong {\text {H}}_{\mathfrak {m}}^t(M/N)$$HIt(M)≅Hmt(M/N) for some submodule N of M with $${\text {dim}}\,(M/N)=t$$dim(M/N)=t.