Auslander–Reiten quiver
= Auslander–Reiten quiver
{c}
For a finite-dimensional <algebra>, the Auslander–Reiten quiver has one vertex for each isomorphism class of finite-dimensional <indecomposable modules>, and its arrows record irreducible module homomorphisms. A homomorphism is irreducible when it is neither a split injection nor a split surjection and every factorization forces the first map to split injectively or the second to split surjectively.