Not every object in the derived category of a ring is Bousfield equivalent to a module

TL;DR

This paper demonstrates that in the derived category of a particular non-Noetherian ring, some objects are not Bousfield equivalent to any module, addressing a question by Dwyer and Palmieri.

Contribution

It provides a counterexample showing not all objects in the derived category are Bousfield equivalent to modules, revealing new structural insights.

Findings

Existence of objects not Bousfield equivalent to modules in D(Λ)

Counterexample to a previous open question

Clarification of Bousfield equivalence in non-Noetherian contexts

Abstract

We consider the derived category of a specific non-Noetherian ring \Lambda, and show that there are objects in D(\Lambda) that are not Bousfield equivalent to any module. This answers a question posed by Dwyer and Palmieri.