Tilting via torsion pairs and almost hereditary noetherian rings

TL;DR

This paper extends the tilting process to finitely presented modules over right coherent rings and characterizes quasi-tilted artin algebras as almost hereditary for all right noetherian rings.

Contribution

It generalizes tilting theory to a broader class of rings and provides a new characterization of quasi-tilted artin algebras.

Findings

Extended tilting process to finitely presented modules over right coherent rings.

Characterized quasi-tilted artin algebras as almost hereditary for all right noetherian rings.

Provided new insights into the structure of modules over these rings.

Abstract

We generalize the tilting process by Happel, Reiten and Smal{\o} to the setting of finitely presented modules over right coherent rings. Moreover, we extend the characterization of quasi-tilted artin algebras as the almost hereditary ones to all right noetherian rings.