HEREDITARY IS HEREDITARY

Belkacem Bendiffalah (1) , Claude Cibils (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

In this note we show that a finite full subcategory of an hereditary small $\mathbb{Z}$-category is hereditary. As a specialization we obtain the result proved in \cite{le,co.ru}, namely that the endomorphism ring of a finitely generated projective module over an hereditary ring is also hereditary, see also \cite{gahe.gopa}. In particular if $A$ is an hereditary ring and $e$ is an idempotent, the ring $eAe$ is also hereditary.

Mots clés: ring; hereditary; category; projective; module

Domaines: Anneaux et algèbres [math.RA]; K-théorie et homologie [math.KT]; Catégories et ensembles [math.CT]

Belkacem Bendiffalah, Claude Cibils. HEREDITARY IS HEREDITARY. 2007. ⟨hal-00124355v1⟩