The stable category of a left hereditary ring

• Alex Martsinkovsky ^[1] ; Dali Zangurashvili ^[2]
  1. [1] Northeastern University

     Northeastern University

     City of Boston, Estados Unidos

     
  2. [2] Tbilisi Centre for Mathematical Sciences, Georgia
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 9 (September 2015), 2015, págs. 4061-4089
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2015.02.007
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• Resumen

  • 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.