On the Gorenstein projective conjecture: IG-projective modules

Abstract

Let [Formula: see text] be a commutative Noetherian local ring. A finitely generated Gorenstein projective [Formula: see text]-module [Formula: see text] is called IG-projective if there exists either an irreducible epimorphism [Formula: see text] or irreducible monomorphism [Formula: see text] with [Formula: see text] being a projective [Formula: see text]-module. In this paper, we give a note on Gorenstein Projective Conjecture: a finitely generated IG-projective module is projective if and only if it is self-orthogonal.