On the finiteness of associated primes of local cohomology modules

Let $R$ be a Noetherian ring, $\mathfrak{a}$ be an ideal of $R$ and $M$ be a finitely generated $R$-module. The aim of this paper is to show that if $t$ is the least integer such that neither $H^t_{\mathfrak{a}}(M)$ nor ${supp}(H^t_{\mathfrak{a}}(M))$ is non-finite, then $H^t_{\mathfrak{a}}(M)$ has finitely many associated primes. This combines the main results of Brodmann and Faghani and independently of Khashyarmanesh and Salarian.