Homological dimensions and special base changes

• Shahab Rajabi ^[1] ; Siamak Yassemi ^[1] ; Blas Torrecillas ^[2]
  1. [1] University of Tehran

     University of Tehran

     Irán

     
  2. [2] Universidad de Almería

     Universidad de Almería

     Almería, España

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 3 ((March 2015)), 2015 (Ejemplar dedicado a: Special Issue in honor of Prof. Hans-Bjørn Foxby), págs. 646-651
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.05.018
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• Resumen

  • We relate the homological behavior of an associative ring R and those of the rings R/xRR/xR and RxRx when x is a regular central element in R . For left weak global dimensions we prove wgldim(R)≤max⁡{1+wgldim(R/xR),wgldim(Rx)}wgldim(R)≤max⁡{1+wgldim(R/xR),wgldim(Rx)} with equality if wgldim(R/xR)wgldim(R/xR) is finite. The key point is a formula for flat dimensions of R -modules: fdRM=max⁡{fdR/xR((R/xR)⊗RLM),fdRxMx}. For left noetherian R we recover results of Li, Van den Bergh and Van Oystaeyen [3] on global and projective dimensions. Similar formulae hold for injective dimensions.