3 problems

Let $S$ be a monoid, and let $\mathcal{F}$-PureMono be the class of pure monomorphisms of right $S$-acts whose Rees quotient is flat. A class of monomorphisms is cellularly generat…

Let $S$ be a monoid, and write $\operatorname{Act}$-$S$ for the category of right $S$-acts. The monoid $S$ is right-reversible when any two principal right ideals intersect. Let…

For a monoid $S$, let $4\mathcal{A}_S(1)4$ and $4\mathcal{A}_S(\aleph_0)4$ denote the classes defined in the preceding results. Non-equality conjecture. There exists a monoid $S$ s…