Closure operators in the categories of modules. Part II (Hereditary and cohereditary operators)

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.