G-dimension and generalized perfect ideals. (Russian) Zbl 0577.13008

The main theorem (proposition 5) is the formula \(G_ K-\dim_ AM=G_{K'}-\dim_{A/I}M+\text{grad}e I\) for a local ring A, an A/I- module M, a certain ideal I of A and certain A-modules K and K’; the dimension \(G_ K\)-dim is a particular case of the G-dimension introduced by H.-B. Foxby [Math. Scand. 31(1972), 267-284 (1973; Zbl 0272.13009)]. The author observes that even in the case of usual G- dimension (i.e. \(K=A)\) the module K’ considered here is not, in general, isomorphic to \(K\otimes_ AA/I\).
Reviewer: G.Dzhanelidze


13D05 Homological dimension and commutative rings
13H99 Local rings and semilocal rings


Zbl 0272.13009