Bousfield lattices of non-Noetherian rings: some quotients and products

TL;DR

This paper explores the structure of Bousfield lattices in tensor triangulated categories, especially for non-Noetherian rings, by developing a framework using derived functors and extending previous results.

Contribution

It introduces a general framework for analyzing Bousfield lattices of derived categories of rings, including non-Noetherian cases, and extends existing results to new classes of rings.

Findings

Relationship between Bousfield lattices of quotients and quotients of lattices

Framework for studying Bousfield lattices via derived functors

Extension of results to non-Noetherian rings

Abstract

In the context of a well generated tensor triangulated category, Section 3 investigates the relationship between the Bousfield lattice of a quotient and quotients of the Bousfield lattice. In Section 4 we develop a general framework to study the Bousfield lattice of the derived category of a commutative or graded-commutative ring, using derived functors induced by extension of scalars. Section 5 applies this work to extend results of Dwyer and Palmieri [DP08] to new non-Noetherian rings.