Rigid modules and ICE-closed subcategories in quiver representations

We introduce image-cokernel-extension-closed (ICE-closed) subcategories of module categories. This class unifies both torsion classes and wide subcategories. show that ICE-closed over the path algebra Dynkin type are in bijection with basic rigid modules precisely some also study natural maps from to terms modules. Finally, we prove number does not depend on orientation quiver, give an explicit formula for each type, which is equal large Schröder A.