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arXiv · 1203.0729

Correspondences of coclosed submodules

Septimiu Crivei·Hatice Inankıl·M. Tamer Koşan·Gabriela Olteanu
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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 $S=End_R(M)$ 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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Septimiu Crivei, Hatice Inankıl, M. Tamer Koşan, Gabriela Olteanu. 2012-03-04. Correspondences of coclosed submodules. https://arxiv.org/abs/1203.0729

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