… Projective dimension and Ext. Let us begin by defining the main topic of concern, projective
dimension. Let M be an 7^-module. Then We can express M as a quotient of a free it-…

… (R)s A, of a family of modules to be M-injective [2]. While R-injective modulesare the same
as injective modules over R, the class of R-projective modules in the sense of Azumaya in …

… We claim that the projective dimension of any indecomposable summand Mg of M as a B-module
is … Consider for example the simple injective module I (4) in example 1 (see Section 4). …

… Because every injective R-module is of projective dimension at most n by hypothesis,
which implies that R is n-Gorenstein by [Citation12, Theorem 9.1.11] since R is commutative …

… of Gorenstein projective R-modules, the class of R-modules of finite projective dimension) is
a … On the other hand, since the class of (FP-)injective modules over a QF ring coincides with …

… Γ -modules (ie, submodules of projective modules), and by … of torsionless Γ -modules of
projective dimension at most one. … a projective module and A A and A M are injective modules, …

… the injective envelope is defined only up to isomorphism. Even if we are already inside a
fixed injective module ER, a submodule AR of ER can have different injective envelopes in ER. …

… modules introduced by Yekutieli. We explain the details by focusing on the projective dimension
… p ) of the class of indecomposable injective modules are parametrized by prime ideals p …

… We investigate ∑-self-orthogonal R-modules and PC -projective dimensions, and … modules,
and the dual classs IC of C- injective modules and the class GIC of GC-injective modules. …

… In this paper, we first study the FP-projective dimension under changes of rings. Let R
and S be right coherent rings (ie, rings such that every finitely generated right ideal is finitely …