The Telescope Conjecture for von Neumann regular rings

TL;DR

This paper proves that all epimorphisms from von Neumann regular rings are universal localizations and confirms the Telescope Conjecture for their unbounded derived categories, advancing understanding in ring and category theory.

Contribution

It establishes that epimorphisms from von Neumann regular rings are universal localizations and verifies the Telescope Conjecture in this context, extending previous results to non-commutative rings.

Findings

Epimorphisms from von Neumann regular rings are universal localizations.

The Telescope Conjecture holds for unbounded derived categories of these rings.

Results apply to both commutative and non-commutative von Neumann regular rings.

Abstract

In this note, we show that any epimorphism originating at a von Neumann regular ring (not necessary commutative) is a universal localization. As an application, we prove that the Telescope Conjecture holds for the unbounded derived categories of von Neumann regular rings (not necessary commutative).