Homological theory of idempotent ideals

Abstract

Let Λ \Lambda be an artin algebra A \mathfrak {A} and a two-sided ideal of Λ \Lambda . Then A \mathfrak {A} is the trace of a projective Λ \Lambda -module P P in Λ \Lambda . We study how the homological properties of the categories of finitely generated modules over the three rings Λ / A \Lambda /\mathfrak {A} , Λ \Lambda and the endomorphism ring of P P are related. We give some applications of the ideas developed in the paper to the study of quasi-hereditary algebras.