Let R be a ring and let simp-R be a representative set of all simple (right R-) modules.
Denote by P< ω the class of all modules which are finitely generated and have finite …

We investigate the relations between finitistic dimensions and restricted flat dimensions
(introduced by Foxby [LW Christensen, H.-B. Foxby, A. Frankild, Restricted homological …

Let $ R $ be a right noetherian ring and let $\mathcal {P}^{<\infty} $ be the class of all finitely
presented modules of finite projective dimension. We prove that findim $ R= n<\infty $ iff …

We prove that (a) if R is a commutative coherent ring, the weak global dimension of R equals
the supremum of the flat (or (FP–) injective) dimensions of the simple R-modules;(b) if R is …

Introduction. For a ring S, let FPD (S) denote the right finitistic projective dimension of S, that
isr the supremum of the finite projective dimensions of right S-modules. If S is a projective …

We investigate two invariants of Noetherian semiperfect rings, namely the depth and a new
invariant we call the “delooping level”. These give lower and upper bounds for the finitistic …

We obtain various characterizations of commutative Noetherian local rings $(R,\fm) $ in
terms of homological dimensions of certain finitely generated modules. For example, we …

For a commutative noetherian ring\(R\), we establish a bijection between the resolving
subcategories consisting of finitely generated\(R\)-modules of finite projective dimension …

We obtain various characterizations of commutative Noetherian local rings (R, m) in terms of
homological dimensions of certain finitely generated modules. Our argument has a series of …

We show that the small and large restricted injective dimensions coincide for Cohen-
Macaulay rings of finite Krull dimension. Based on this, and inspired by the recent work of …