On ideal closure operators of \(M\)-sets (Q874850)

The author studies closure operators (in the not-necessarily-idempotent sense of \textit{D.~Dikranjan, E.~Giuli} and \textit{W.~Tholen}) on the category of \(M\)-sets for a monoid \(M\). He shows that every right ideal of \(M\) gives rise to such a closure operator, although there is no loss of generality in restricting to two-sided ideals since a right ideal and its two-sided hull generate the same closure operator. He also makes some elementary observations about the lattice formed by the closure operators which arise in this way.