A trivializability principle for local rings is described which leads to a form of weak algorithm for local semifirs with a finitely generated maximal ideal whose powers meet in zero.

Let R be a parabolic subgroup in $G{L}_n$. It acts on its unipotent radical $R_u$ and on any unipotent normal subgroup U via conjugation. Let Λ be the path algebra $k_t$ of a directed Dynkin quiver of type with t vertices and B a subbimodule of the radical of Λ viewed as a Λ-bimodule. Each parabolic subgroup R is the group of automorphisms of an algebra Λ(d), which is Morita equivalent to Λ. The action of R on U can be described using matrices over the bimodule B. The advantage of this description is that each...