Hereditary stable tubes in module categories

The concepts of a self-hereditary stable tube $\mathcal T$ and a hereditary stable tube $\mathcal T$ in a module category $\mod\,A$ are introduced, where $A$ is a finite dimensional algebra over an algebraically closed field. Characterisations of self-hereditary stable tubes and hereditary stable tubes are given, and illustrative examples of such tubes are presented. Some open problems are presented.