All solid rings

TL;DR

This paper characterizes the solid rings of the fourth type explicitly, completing a longstanding problem and providing methods to identify and compute the core of such rings.

Contribution

It offers a complete explicit characterization of the solid rings of the fourth type and introduces criteria for finding and computing the core of rings.

Findings

Explicit characterization of the solid rings of the fourth type

Criteria for identifying the core of a ring

Explicit computations of ring cores

Abstract

We give an explicit characterization of the solid rings of the fourth type, finishing a work by Bousfield and Kan in the 1970s. As a consequence of our methods, we give criteria to find the core of a ring and explicitly compute the core of some rings.