A summary of the key aspects of ideal approximation theory is given, beginning with a review of the motivating results and arguments from the classical approximation theory. The notion of a complete ideal cotorsion pair is motivated by a proof of Salce's Lemma for Ideals. This is used to establish a bijective correspondence between complete ideal cotorsion pairs in a category R-Mod of modules with the subfunctors of Ext that have enough special injective (resp., projective) morphisms. Three examples are given of how a subfunctor of Ext that has enough injective morphisms gives rise to a complete ideal cotorsion pair. For a QF artin algebra, it is proved that every almost split sequence arises as the pullback along an Auslander Reiten (AR) phantom morphism.
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