Geodesic
Closure operators in the categories of modules. Part I (Weakly hereditary and idempotent operators)
Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 213-228

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In this work the closure operators of a category of modules $R$-Mod are studied. Every closure operator $C$ of $R$-Mod defines two functions $\mathcal{F}_1^{C}$ and $\mathcal{F}_2^{C}$, which in every module $M$ distinguish the set of $C$-dense submodules $\mathcal{F}_1^{C}(M)$ and the set of $C$-closed submodules $\mathcal{F}_2^{C}(M)$. By means of these functions three types of closure operators are described: 1) weakly hereditary; 2) idempotent; 3) weakly hereditary and idempotent.
Keywords: ring, lattice, preradical, closure operator, lattice of submodules, dense submodule, closed submodule.
Mots-clés : module 
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     author = {A. I. Kashu},
     title = {Closure operators in the categories of modules. {Part} {I} {(Weakly} hereditary and idempotent operators)},
     journal = {Algebra and discrete mathematics},
     pages = {213--228},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2013_15_2_a6/}
}
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A. I. Kashu. Closure operators in the categories of modules. Part I (Weakly hereditary and idempotent operators). Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 213-228. http://geodesic.mathdoc.fr/item/ADM_2013_15_2_a6/