Let $A=KQ/I$ be a quiver algebra such that the admissible ideal $I$ contains only the field elements $0,1$ and $-1$.
Question: Is it true for every basic idempotent $e$ that the algebra $eAe$ is isomorphic to a quiver algebra such that the admissible ideal $I$ contains only the field elements $0,1$ and $-1$?
Question: Is it true in case $A$ is QF-3 and $e$ is such that $eA$ is the basis version of a minimal faithful projective-injective $A$-module?