In 1966, Auslander introduced the notion of the G-dimension of a finitely generated module over a Cohen-Macaulay noetherian ring and found the basic properties of these dimensions. His results were valid over a local Cohen-Macaulay ring admitting a dualizing module (also see Auslander and Bridger (Mem. Amer. Math. Soc., vol. 94, 1969)). Enochs and Jenda attempted to dualize the notion of G-dime...

We give a short and simple argument that proves, in a uniform way, the Auslander-Buchsbaum formula, relating depth and projective dimension, and the Auslander-Bridger formula, relating depth and G-dimension. Moreover, the same type of argument quickly reproves the fact that, in the degrees above the codepth, the syzygy modules of a finite module over a commutative local ring have no free summan...

In [2, Section 1.6] Peskine and Szpiro prove a theorem on adic approximations of finite free resolutions over local rings which, together with M. Artin's Approximation Theorem [1], allows them to "descend" modules of finite projective dimension over the completions of certain local rings to modules of finite projective dimension over finite etale extensions of those rings. In this note we will ...

It is well-known that a ring R is semiperfect if and only if RR (or RR) is a supplemented module. Considering weak supplements instead of supplements we show that weakly supplemented modules M are semilocal (i.e., M/Rad(M) is semisimple) and that R is a semilocal ring if and only if RR (or RR) is weakly supplemented. In this context the notion of finite hollow dimension (or finite dual Goldie d...

The finitistic dimension conjecture says that the projective dimension of finitely generated modules over an Artin algebra is bounded when finite. The conjecture is known for algebras of representation dimension 3, for modules of Loevey length 2 and for stratifying systems with at most 2 indecomposable modules of infinite projective dimension (Huard, Lanzilotta, Mendoza [4]). We would like to i...

For finitely generated module M over a local ring R, the conventional notions of complete intersection dimension CI-dimRM and CohenMacaulay dimension CM-dimRM do not extend to cover the case of infinitely generated modules. In this paper we introduce similar invariants for not necessarily finitely generated modules, (namely, complete intersection flat and Cohen-Macaulay flat dimensions) which f...

— We propose a definition of (polarized) wild twistor D-modules, generalizing to objects with irregular singularities that of (polarized) regular twistor D-modules. We give a precise analysis in dimension one. Résumé. — Nous proposons une définition de D-module sauvage avec structure de twisteur (polarisée), généralisant celle des D-modules réguliers avec structure de twisteur (polarisée). Nous...