… In particular, Herzog generalized in [19] the phantom morphism to the category of left R-… of
a morphism of short exact sequences, we prove that a morphism ψ is Gorenstein cophantom if …

… class of Gorenstein injective Phantom morphisms been closed … a morphism φ: X→X′ of
R-modules is higher Gorenstein injective Phantom morphism if and only if there is a Gorenstein …

… It is proved that a morphism f : G 1 → G 2 is Gorenstein flat if and only if f is a
monomorphism and G 1 , G 2 and Coker f are Gorenstein flat R-modules. Then, we show …

… Also instead of S/mS to be regular as it is the required in (7.36) Theorem, [6], here we
need S/mS to be a Gorenstein ring of zero dimension. But, we have a relaxation on these …

… by the (Kaplansky) class of phantom morphisms in the (Grothendieck) category of … morphism
ϕ: Z0(F•) → M, where Z0(F•) is Gorenstein flat. We now argue that ϕ is a Gorenstein flat …

… , phantom and cophantom morphisms may be viewed as the morphism versions of flat and …
We have known that phantom and cophantom morphisms admit nice properties when the ring …

… Then a morphism f : X → Y in T is phantom if and only if Q(f) is zero. In particular, A → B →
C … GFn (resp., GIn) of Gorenstein flat (resp., Gorenstein injective) dimension at most n also …

… 1 f n − 2 ⋯ f 0 a nonzero morphism. We note that a converse of the Ghost Lemma for D b f ( R
) has … Since f n − 1 f n − 2 ⋯ f 0 is a nonzero morphism we obtain that level R P M ⩾ n by the …

… 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 recall that phantom morphisms were introduced by McGibbon [Mc] for use in topology
to … Let A = mod-Λ and let B = Gprj -Λ be the full subcategory of A consisting of all Gorenstein-…