… a relative Γ-pure injective envelope. Also, he has shown that the relative Γ-pure injectivity
coincides with the relative Γ-… X -covers) exist, then they are unique up to isomorphism. Also, it is …

… of pure-injective modules and pure-projective modules are more useful than that of injective
modules … (see [1]) studied envelopes and covers by modules of finite injective and projective …

… of relative projectivity and relative injectivity that extend the notions of quasi-projective and
quasi-injective … -projective covers implies that of projective covers." As our final application of …

… Ninjective, then M is weakly N / K-injective for each submodule K ofN. In particular, M is weakly
injective if and only if M is weakly Rn-injective … having a projective cover are the projective …

… as a “relative” version of sheaf cohomology. Due to the result that injectivity of sheaves of …
Externally, this yields an open covering of X such that we have, for each member U of that …

… n -injective and FP n -flat complexes. We first prove the existence of special FP n -injective
preenvelopes and FP n -flat covers, which allow to consider FP n -injective coresolutions and …

… FP-injective cover α :A → B with A injective. By Proposition 2.4, M is FI-injective. Now let K be
an … Since there exists a monic FP-injective cover g :G → M by (3), we have K ⊕ G ∼= F by …

… We are interested in relative uniform cyclic covers f : X → P of degree r, where P → S is a …
i: L⊗r → OP , which remains injective when restricted to any geometric fiber. The morphisms …

… injective modules is both covering and enveloping over any commutative noetherian ring R
such that the character modules of Gorenstein injective … RG is Gorenstein injective. Another …

… flat injective) modules (see [7, 8, 9]). In particular, Guo [9] defined the relative injective envelopes
(resp., projective covers… module over extension of Artin algebras has a relative injective …