The Gabriel–Roiter measure for radical‐square zero algebras

Let Λ be a radical‐square zero algebra over an algebraically closed field k with radical , and let Γ = (Λ / τ0τΛ / τ)be the associated hereditary algebra. There is an explicit functor F : mod Λ → mod Γ, which induces a stable equivalence. In this paper, it will be proved that the functor F preserves the Gabriel–Roiter (GR) measures and the GR factors. Thus the GR measure for Λ can be studied by the use of F and known facts for hereditary algebras. In particular, the middle terms of the Auslander–Reiten sequences ending at the GR factors and the relationship between the preprojective partition for Λ and the take‐off Λ‐modules will be investigated.