Large Bricks and Join-irreducible torsionfree classes

TL;DR

This paper demonstrates that each join-irreducible torsionfree class over an artinian ring can be cogenerated by a single brick, extending previous characterizations of such classes.

Contribution

It extends the characterization of join-irreducible torsionfree classes by showing they are cogenerated by a single brick, even if not finitely generated.

Findings

Every join-irreducible torsionfree class is cogenerated by a brick.

Extension of previous characterizations of torsionfree classes.

Provides a new perspective on the structure of torsionfree classes.

Abstract

We show that every join-irreducible torsionfree class in the category of finitely generated modules over an artinian ring is cogenerated by a single (not necessarily finitely generated) brick. This is a partial extension of the characterisation of completely join-irreducible torsionfree classes given by Barnard, Carroll and Zhu.