Homological properties and finiteness of reducing invariants

We study reducing invariants of modules related to certain homological properties. For modules of finite reducing projective dimension, we establish grade inequalities. We prove that if $\mathbb{P}$ is the (uniform) Auslander condition, or the generalized Auslander–Reiten conjecture, or dependence of the total reflexivity conditions, then a module satisfies $\mathbb{P}$ provided that it has finite reducing invariant with respect to $\mathbb{P}$.