For left artinian rings with a suitable semisimple subring, the singularity category is triangle equivalent to the stable module category of the zeroth component of the Leavitt ring, which is an FC ring.
Auslander , Representation Dimension of Artin Algebras, Math
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The singularity category as a stable module category
For left artinian rings with a suitable semisimple subring, the singularity category is triangle equivalent to the stable module category of the zeroth component of the Leavitt ring, which is an FC ring.