# When the kernel of a complete hereditary cotorsion pair is the additive closure of a tilting module

## TL;DR

This paper investigates conditions under which the kernel of a complete hereditary cotorsion pair aligns with the additive closure of a tilting module, with applications to finitistic dimension, Wakamatsu tilting modules, and Gorenstein rings.

## Contribution

It provides new characterizations and conditions linking cotorsion pairs, tilting modules, and properties of Gorenstein rings, extending existing theory.

## Key findings

- Characterization of when the finitistic dimension is finite.
- Equivalent conditions for Wakamatsu tilting modules to be tilting.
- New characterizations of Gorenstein rings.

## Abstract

In this paper, we study when the kernel of a complete hereditary cotorsion pair is the additive closure of a tilting module. Applications go in three directions. The first is to characterize when the little finitistic dimension is finite. The second is to obtain equivalent formulations for a Wakamatsu tilting module to be a tilting module. The third is to give some new characterizations of Gorenstein rings.