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 $\psi (M)=0$ (or equivalently $\varphi (M)=0$) for all finitely generated right $R$-modules $M$, where $\psi ,\varphi :\mathrm{mod}R\to \mathbb{N}$ are functions defined by Igusa and Todorov. In particular, an artin algebra $\Lambda$ is self-injective if and only if $\varphi (M)=0$ for all finitely generated right $\Lambda$-modules $M$.

5 pages

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