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 GC-perfection is preserved by relative Auslander transpose, and how to numerically characterize horizontally linked modules. Moreover, we show how to produce reduced -perfect modules that are also C-k-torsionless ( is an integer) but fail to be -perfect, and we illustrate that, unlike the usual grade, the relative reduced grade depends on the choice of C.
2020 Mathematics Subject Classification:
Acknowledgments
The authors also wish to thank the anonymous referee for helpful comments and suggestions, particularly for correcting an inaccuracy in the proof of Corollary 3.14.
Disclosure statement
No potential competing interest was reported by the author(s).