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To an artin algebra with radical square zero, a regular algebra in the senseof von Neumann and a family of invertible bimodules over the regular algebraare associated. These data describe completely, as a triangulated category, thesingularity category of the artin algebra. A criterion on the Hom-finiteness ofthe singularity category is given in terms of the valued quiver of the artinalgebra.

The singularity category of an algebra with radical square zero