PRECOVERS AND ORTHOGONALITY IN THE STABLE MODULE CATEGORY
IOANNIS EMMANOUIL
Abstract. We show that any module admits a presentation as the quotient of a Gorenstein projective module by a submodule which is itself right orthogonal, with respect to the standard Ext1 pairing, to the class of Gorenstein projective modules of type FP#. For that purpose, we use the concept of orthogonality in the stable module category and examine the orthogonal pair which is induced therein by the class of completely finitary Gorenstein projective modules.
Contents
0. Introduction 1
1. Preliminaries 4
2. Hyperfinite extensions of Gorenstein projective modules 6
3. Stably finitely presented modules and orthogonality 11
4. Completely finitary Gorenstein projective modules 16
References 19