Abstract Assume that (X, O _X)(X, OX) is an arbitrary scheme. The concept of the big (resp.
little) finitistic flat dimension FFD (X)(resp. fFD (X)) of X will be introduced. It is shown that if X …

Let R be a commutative ring with identity. The small finitistic dimension fPD (R) of R is
defined to be the supremum of projective dimensions of R-modules with finite projective …

Let R be a noetherian ring and S an excellent extension of R. cid (M) denotes the copure
injective dimension of M and cfd (M) denotes the copure flat dimension of M. We prove that if …

Let R be a commutative ring with identity. Denote by FPR (R) the set of all R-modules
admitting a finite projective resolution consisting of finitely generated projective modules …

In this article, we study the weak global dimension of coherent rings in terms of the left FP-
injective resolutions of modules. Let R be a left coherent ring and ℱ ℐ the class of all FP …

Let R be a commutative coherent ring and wD (R) denote the weak global dimension of R.
We prove that for an integer n≥ 2 the following are equivalent:.(a) wD (R) n;.(b) FP-idM⊗ …

Let R be any ring. A right R-module M is called n-copure projective if Ext1 (M, N)= 0 for any
right R-module N with fd (N)≤ n, and M is said to be strongly copure projective if Ext i (M, F) …

The finitistic global dimensions lf PD (R), l FPD (R), and l FID (R) are defined for a ring R. We
obtain the following results for R semiprimary with Jacobson radical N. C is a simple left R …

Bounds are determined for the finitistic dimensions of one-sided almost serial rings in terms
of the projective dimensions of the simple modules of finite projective dimension and in …

It is well known that, given a ring R, if M is an R-module such that pdR (M)<∞, then GidR
(M)= idR (M)(Holm, 2004). This shows in particular that if R is a Noetherian ring such that …