Correspondences of coclosed submodules
  We establish an order-preserving bijective correspondence between the sets of coclosed elements of some bounded lattices related by suitable Galois connections. As an application, we deduce that if $M$ is a finitely generated quasi-projective left $R$-module with $S=End_R(M)$ and $N$ is an $M$-generated left $R$-module, then there exists an order-preserving bijective correspondence between the sets of coclosed left $R$-submodules of $N$ and coclosed left $S$-submodules of $Hom_R(M,N)$. 
Septimiu Crivei, Hatice Inank{\i}l, M. Tamer Ko\c{s}an and Gabriela   Olteanu
math.RA