Hereditary stable tubes in module categories

Abstract

The concepts of a   self-hereditary stable  tube \({\cal T}\) and a hereditary stable  tube \({\cal T}\)   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.