Correspondences of coclosed submodules

Abstract

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 $S=En{d}_R(M)$ 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 $Ho{m}_R(M,N)$.

10 pages; to appear in Comm. Algebra