Correspondences of coclosed submodules

Details Correspondences of coclosed submodules Correspondences of coclosed submodules

2012-03-04

arxiv.org/abs/1203.0729v1

Mathematics

Rings and Algebras

10 pages; to appear in Comm. Algebra

Scientific paper

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 $Hom_R(M,N)$.

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