On reduced G-perfection and horizontal linkage

Abstract

In this paper, we contribute to the theory of reduced G-perfection and horizontal linkage of modules over a commutative, Noetherian (typically, local) ring R, in the general setting where properties and operations are considered relatively to a semidualizing module C. We investigate when reduced G C -perfection is preserved by relative Auslander transpose, and how to numerically characterize horizontally linked modules. Moreover, we show how to produce reduced G C -perfect modules that are also C-k-torsionless ( k ≥ 0 is an integer) but fail to be G C -perfect, and we illustrate that, unlike the usual grade, the relative reduced grade depends on the choice of C.