# The stable category of a left hereditary ring

@article{Martsinkovsky2014TheSC, title={The stable category of a left hereditary ring}, author={Alex Martsinkovsky and Dali Zangurashvili}, journal={arXiv: Rings and Algebras}, year={2014} }

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.

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