ABSTRACT
Let M be a left module over a unital ring R and let £ be the endomorphism ring of M. The object of this paper is to construct Galois connections between the lattice of ideals of £ and the lattice of fully invariant submodules of M. Using the consequent isomorphism between the lattices of Galois closed ideals and closed submodules, we are able to deduce structural properties of £ in terms of those of M and vice versa.
