The stable category of a left hereditary ring
  The (co)completeness problem for the (projectively) stable module category of an associative ring is studied. (Normal) monomorphisms and (normal) epimorphisms in such a category are characterized. As an application, we give a criterion for the stable category of a left hereditary ring to be abelian. By a structure theorem of Colby-Rutter, this leads to an explicit description of all such rings. 
Alex Martsinkovsky and Dali Zangurashvili
math.RA math.CT math.RT