The Igusa-Todorov $\varphi$-dimension on Morita context algebras

Abstract

In this article we prove that, under certain hypotheses, Morita context algebras that have zero bimodule morphisms have finite $\varphi$-dimension. We also study the behaviour of the $\varphi$-dimension for an algebra and its opposite. In particular we show that the $\varphi$-dimension of an Artin algebra is not symmetric, i.e. there exists a finite dimensional algebra $A$ such that $\varphi \dim (A)\ne \varphi \dim (A^{op})$.