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

Abstract

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.