Injective representations of bound quiver algebras

Abstract

Let [Formula: see text] be a ring and [Formula: see text] be a finite quiver. We give an explicit formula for the injective envelopes and projective precovers in the category [Formula: see text] of bound representations of [Formula: see text] by left [Formula: see text]-modules, where [Formula: see text] is a combination of monomial and commutativity relations. Some applications will be provided. In particular, it is shown that if [Formula: see text] is acyclic and [Formula: see text] is an Iwanaga-Gorenstein ring, then so are these bound quiver algebras.