%0 Journal Article
%T Self-injective right artinian rings and Igusa Todorov functions
%A Fran\ccois Huard
%A Marcelo Lanzilotta
%J Mathematics
%D 2011
%I arXiv
%X We show that a right artinian ring $R$ is right self-injective if and only if $\psi(M)=0$ (or equivalently $\phi(M)=0$) for all finitely generated right $R$-modules $M$, where $\psi, \phi : \mod R \to \mathbb N$ are functions defined by Igusa and Todorov. In particular, an artin algebra $\Lambda$ is self-injective if and only if $\phi(M)=0$ for all finitely generated right $\Lambda$-modules $M$.
%U http://arxiv.org/abs/1101.1936v1