(untitled) (Communications in Mathematical Research, 2020)
A unitary right R-module M_R satisfies acc on d-annihilators if for every sequence (a_n)_n of elements of R the ascending chain Ann_M(a_1)Ann_M(a_1a_2)Ann_M(a_1a_2a_3)… of submodules of M_R stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions, the Ore extension module M[x]_R[x;α,δ] over the Ore extension ring R[x; α,δ] satisfies acc on d-annihilators if and only if the module M_R satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.