… finitistic projective dimension of R… dimensions of R in terms of P1-injective modules. In
particular, we prove the following formula for the weak global dimension and the global dimension …

… (G C -projective and G C -injective dimensions) of the module… C -projective dimension of a
ring and the global dimension of … -Gorenstein projective and injective modules and dimensions…

… left module M if M is a faithful injective module and if M appears as a direct summand of
every faithful module. It is clear that M must be protective, for the ring itself is a faithful protective …

… projective right R-module is projective if and only if all (n, 0)-projective right R-modules are of
projective dimension … any (n − m, d)-projective right R-module M (see Theorem 4.4). Dually, …

… N-injective and weakly injective modules are … injective right A-module is weakly projective.
We also study those rings over which every weakly projective right module is weakly injective. …

… All modules will be left R-modules unless otherwise specified… all modules with injective
dimension and projective dimension … contain all injective and projective modules, respectively, so …

… dimension at most one, and by $$\mathcal{R}_A$$ the full subcategory of ind A formed by
the modules X whose all successors in ind A have injective dimension at most one. Recently, …

… of modules with finite projective dimension is based on a number of formal properties. Recall
that a class X of L-modules is … of Mod L containing all injective modules. Moreover, for any L-…

… injective modules in σ[M 1 ] (σ[M 2 ]) and injective modules in σ[… injective modules in σ[M 1
] (σ[M 2 ]) and injective modules in σ[… σ-projective dimension and projective dimension in R M. …

… Since injective modules form a subclass of C', we can form an exact sequence … C-projective
dimension r (denoted C-projdimM = T). iC-projective resolutions and iC-projective dimension …