Systems of submodules and an isomorphism problem for Auslander-Reiten quivers. (Q953989)

For representations of partially ordered sets \(\Omega\) over commutative local rings \(R\) of finite radical length, the dependence of Auslander-Reiten components on constants in \(R\) is considered. According to its \(R\)-module structure, a type is associated to every \(\Omega\)-representation. For example, if \(\mathcal L\) is a slice in a component \(\Gamma\) of the Auslander-Reiten quiver, it is shown that the types of the indecomposables in \(\Gamma\) are determined by the modules in \(\mathcal L\). Under a certain condition it is shown that the component \(\Gamma\) is determined by the structure of \(\mathcal L\).