Resumen de Homological dimensions and special base changes

Shahab Rajabi, Siamak Yassemi, Blas Torrecillas Jover

• 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.