Bricks and the Lattice of Torsion Classes

Last week, Yucong introduced the lattice of torsion classes. This coming week, we’ll examine several properties of the lattice of torsion classes. We’ll characterize the completely join irreducible elements and, time permitting, prove that the lattice of torsion classes is completely semi-distributive. Underlying both of these properties are “bricks”, a special kind of indecomposable module.

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Date published: Wednesday, February 25, 2026