Geodesic
Closure operators in the categories of modules. Part II (Hereditary and cohereditary operators)
Algebra and discrete mathematics, Tome 16 (2013) no. 1, pp. 81-95

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This work is a continuation of the paper [1] (Part I), in which the weakly hereditary and idempotent closure operators of the category $R$-Mod are described. Using the results of [1], in this part the other classes of closure operators $C$ are characterized by the associated functions $\mathcal{F}_1^{C}$ and $\mathcal{F}_2^{C}$ which separate in every module $M \in R$-Mod the sets of $C$-dense submodules and $C$-closed submodules. This method is applied to the classes of hereditary, maximal, minimal and cohereditary closure operators.
Keywords: ring, preradical, closure operator, dense submodule, closed submodule, hereditary (cohereditary) closure operator.
Mots-clés : module 
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     title = {Closure operators in the categories of modules. {Part} {II} {(Hereditary} and cohereditary operators)},
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A. I. Kashu. Closure operators in the categories of modules. Part II (Hereditary and cohereditary operators). Algebra and discrete mathematics, Tome 16 (2013) no. 1, pp. 81-95. http://geodesic.mathdoc.fr/item/ADM_2013_16_1_a8/