Annihilators and attached primes of local cohomology modules with respect to a system of ideals

Let Φ be a system of ideals of a commutative Noetherian ring, we study the annihilators and attached primes of local cohomology modules with respect to a system of ideals. We prove that if M is a non-zero finitely generated R-module of finite dimension d and Φ is a system of ideals, then Att(HdΦ(M))={p∈AssM∣cd(Φ,R/p)=d}. Moreover, if the cohomology dimension of M with respect to Φ is dimM−1, then Att(HdimM−1Φ(M))={p∈SuppM∣cd(Φ,R/p)=dimM−1}.