Theory of linkage, Gorenstein dimension and two semidualizing modules

Abstract

Let [Formula: see text] be a semiperfect commutative Noetherian ring with identity and [Formula: see text] be semidualizing [Formula: see text]-modules. We study the theory of linkage with respect to [Formula: see text] for modules of finite [Formula: see text]-dimension. For a module which is horizontally linked with respect to [Formula: see text], the connections of its invariants reduced grade with respect to [Formula: see text], [Formula: see text]-dimension and depth are discussed. Along the way, we provide a characterization of horizontally linked modules with respect to [Formula: see text] of [Formula: see text]-dimension zero.