Abstract
Let $$\mathcal {X}$$, $$\mathcal {U}$$ and $$\mathcal {Z}$$ be classes of left R-modules, $$\mathcal {W}$$ be a class of right R-modules and $$\mathcal {X}\subseteq \mathcal {U}$$. In this paper, we investigate the relationship between $$\mathcal {Z}$$-proper (resp. $$\mathcal {Z}$$-coproper, $$\mathcal {W}$$-pure) $$\mathcal {U}$$-(co)resolutions and $$\mathcal {Z}$$-proper (resp. $$\mathcal {Z}$$-coproper, $$\mathcal {W}$$-pure) $$\mathcal {X}$$-(co)resolutions. As applications, we give an affirmative answer to the stability question on Gorenstein classes of modules, which unify the corresponding results possessed by some known Gorenstein classes of modules.
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