A note on the singularity category of an endomorphism ring

TL;DR

This paper introduces the concept of partial resolution of a ring via endomorphism rings of generators, showing how it affects the singularity category and providing examples and implications.

Contribution

It defines partial resolution of rings and demonstrates how it influences the singularity category, offering new insights into ring theory and singularity analysis.

Findings

Singularity category of partial resolution is a quotient of the original

Provides examples illustrating the theoretical results

Establishes a framework for understanding ring singularities

Abstract

We propose the notion of partial resolution of a ring, which is by definition the endomorphism ring of a certain generator of the given ring. We prove that the singularity category of the partial resolution is a quotient of the singularity category of the given ring. Consequences and examples are given.