| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4596099 | Journal of Pure and Applied Algebra | 2015 | 6 Pages |
Abstract
We relate the homological behavior of an associative ring R and those of the rings R/xR and Rx when x is a regular central element in R. For left weak global dimensions we prove wgldim(R)â¤maxâ¡{1+wgldim(R/xR),wgldim(Rx)} with equality if wgldim(R/xR) is finite. The key point is a formula for flat dimensions of R-modules: fdRM=maxâ¡{fdR/xR((R/xR)âRLM),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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Shahab Rajabi, Blas Torrecillas, Siamak Yassemi,