Small-Essential Submodules and Morita Duality.

We introduce and investigate e-small and s-essential submodules, and prove that Rade(M)= ∩{ N ⊴ M / N is maximal in M }=∑ { N ⊆ M / N ≪e M} and Socs(M)=∑{ N ≪ M / N is minimal in M }=∩{ L ≤ M / L⊴sM}. As an application, we introduce the e-gH and s-wcH pairs of modules, and show that they are dual to each other under Morita duality. [ABSTRACT FROM AUTHOR]