Some Results on Modules Satisfying ACCR

Let M be a module over a one- dimensional Laskerian domain R. In this note we determine when M satisfies the condition that every ascending chain of submodules of the form W: B ⊆ W: B² ⊆ W:B³ ⊆ … terminates for every submodule W of M and every finitely generated ideal B of R.