Quasi-hereditary rings are closed under taking block extensions

TL;DR

This paper establishes a sufficient condition for Morita context rings to be quasi-hereditary and demonstrates that block extensions of such rings preserve this property, expanding understanding of their structural stability.

Contribution

It introduces a new criterion for Morita context rings to be quasi-hereditary and proves that block extensions of quasi-hereditary rings are also quasi-hereditary.

Findings

Morita context rings can be quasi-hereditary under certain conditions

Block extensions of quasi-hereditary rings remain quasi-hereditary

Provides a new perspective on the stability of quasi-hereditary property

Abstract

In this paper, we give a sufficient condition for Morita context rings to be quasi-hereditary. As an application, we show that each block extension of a quasi-hereditary ring is also quasi-hereditary.