From CM-finite to CM-free

• Fan Kong ^[1] ; Pu Zhang ^[2]
  1. [1] Chongqing University

     Chongqing University

     China

     
  2. [2] Shanghai Jiao Tong University

     Shanghai Jiao Tong University

     China

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 220, Nº 2 (February 2016), 2016, págs. 782-801
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2015.07.016
• Enlaces
  • Texto completo
• Resumen

  • We prove a generalization of the stability for Gorenstein categories in [36] and [24]; and show that the relative Auslander algebra of a CM-finite algebra is CM-free. On the other hand, we describe the bounded derived category, and the Gorenstein defect category introduced in [11], via Gorenstein-projective objects; and we show that the Gorenstein defect category of a CM-finite algebra is triangle-equivalent to the singularity category of its relative Auslander algebra.