… In this case, a morphism f: X→ A is a phantom morphism if … injective module may be taken to
be the injective envelope of … to a P-Ext-phantom as a pure phantom morphism. The complete …

… -pure morphisms and 그-phantom morphisms in this paper, which are … is said to be a
cophantom morphism or Ext-phantom … M has a phantom envelope, ϕ is a phantom morphism and …

… For an R-module M, E(M) denotes the injective envelope of M, the character module Hom ℤ
(M… direct limits if every right R-module has an ℱ ℐ n -cover with the unique mapping property. …

… Envelopes and covers provide common frames for a number of classical notions such as …
envelopes and projective covers, and turn out to be extremely fruitful for general module theory …

… phantom cover for each R-module, first, we show that the class of G F ‐ phantom morphisms
is a covering … if and only if every R -module has a flat pre-envelope. Combine the above two …

… pure, phantom and Ext -phantom morphisms of modules. … B -covers ( B -envelopes) may
not exist in general, but if they … M → ψ N is an absolutely pure envelope in R-Mod. Let ( N → …

… We also show how pure-injective envelopes may be used to construct a minimal flat …
As in the case of functors, flat modules may be characterized (cf. [14, Theorem 1.4]) as direct …

… module category, an effective approach to study the existence of (pre)envelopes and (pre)covers
of a module … existence theorems for (pre)envelopes and (pre)covers (in the sense of …

… Some characterizations of n-phantom morphisms and n-Ext-phantom morphisms. … -phantom
and n-Ext-phantom of morphisms in short exact sequence and pullback diagram of modules. …

… 作为应用,本文第二部分利用(n,d)-phantom 与(n,d)-Ext-phantom 态射给出了右(n,d)-环,右n-…
On covers and envelopes in some functor categories[J]. Commun Algebra,41(5):1655-1684. …