Self-injective Right Artinian Rings and Igusa Todorov Functions

Abstract

We show that a right artinian ring R is right self-injective if and only if ψ(M) = 0 (or equivalently ϕ(M) = 0) for all finitely generated right R-modules M, where ψ, $\phi :\!\!\!\! \mod R \to \mathbb N$ are functions defined by Igusa and Todorov. In particular, an artin algebra Λ is self-injective if and only if ϕ(M) = 0 for all finitely generated right Λ-modules M.