2014/08/13 by Alex Martsinkovsky, Dali Zangurashvili, Martsinkovsky, Alex +1 · 1 citation
Mathematics · #16D90 #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.CT #math.RA #math.RT #msc:16D90
paper · pdf · doi:10.48550/arxiv.1408.2904
31 pages. Corrected typos and minor editorial changes to improve readability
arxiv created 2015/01/04 · arxiv updated 2015/01/06
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.