… based on phantom envelopes and Ext-phantom covers of … replacing phantom and Ext-phantom
with n-phantom and n-… of n-phantom morphism [14], which is a higher dimensional …

… Ext-phantom morphisms are also called cophantom morphisms in [14]. … We note that the
existence of Ext-phantom preenvelopes is a special case of [14, Theorems 32 and 33]. In Sect. 2 …

… right module A and α is said to be an n-Ext-phantom if Extn(A, α) is 0 for every … phantom
(resp., a 1-Ext-phantom) morphism if and only if α is a phantom (resp., an Ext-phantom) morphism…

… cophantom morphism or Ext-phantom morphism [15, 22] if the induced … morphism versions
of flat and absolutely pure modules. We have known that phantom and cophantom morphisms …

… Phantom morphisms been closed under direct product and ME-extensions in H(R). It is proved
that a morphism φ: X→X′ of R-modules is higher … 了n-Phantom态射和n-Ext-Phantom态射…

… In this paper, (higher) Gorenstein flat phantom morphisms over rings will be introduced
and studied. To study their relationship, a characterization of Gorenstein flat objects in …

… We call such a morphism f, as an n-Ext-phantom morphism. In Section 7, we introduce a
composition operator “◦” on Extn /P. It is shown that this operator is associative and distributive …

We investigate preenvelopes and precovers in the category $$_{R}{\mathcal {E}}$$ R E of
short exact sequences of left R-modules. Let $${\mathfrak {C}}$$ C be a class of left R-…

… injective Phantom morphism and higher Gorenstein injective Phantom morphism have been
… 文献[8]引入了n-Phantom态射和n-Ext-Phantom态射的概念,证明了:在R-Mod中,f:M→N是n-…

… and preenvelopes by phantom and Ext-phantom morphisms[J]… Higher phantom and Ext-phantom
morphisms[J]. J Algebra … Higher phantom morphisms with respect to a subfunctor of Ext[…