The Igusa-Todorov \(\phi \)-Dimension on Morita Context Algebras

Abstract

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