We study the problem of existence of essential indecomposable submodules of direct sums of copies of the ring of quotients of Ore domains. We provide, for each Ore domain $D$, with at least three non-associate irreducibles, a lower bound for the supremum of all cardinals $\kappa$ such that the direct sum of $\kappa$ copies of the ring of quotients of $D$ contains indecomposable essential $D$-submodules, and a lower bound for the number of times this bound is attained up to isomorphisms. We provide examples illustrating these results.
Categories: math.RA