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We show that an adaptation of Landrock's Lemma for symmetric algebras alsoholds for cellular algebras and BGG algebras. This is a result relating theradical layers of any two projective modules. The reason it holds in oursetting is that there is a duality between injective hulls and projectivecovers. As a corollary we deduce that BGG reciprocity respects Loewy structure.

A Reciprocity Result for Projective Indecomposable Modules of Cellular Algebras and BGG Algebras