This work introduces phantom ideals linked to exact sequences in modules, highlighting their role in module categories.
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.
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Rasool Hafezi (2026) studied this question.
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