Relative phantom morphisms

In this paper, motivated by the notion of phantom ideals in the category of modules, we develop a general construction which associates phantom ideals of morphisms to special preenveloping classes of modules. As applications, we introduce two new ideals of morphisms arising from [Formula: see text]-pure exact sequences and from Hom-exact sequences with respect to modules of finite projective dimension, and we obtain complete cotorsion pairs of ideals in both cases.