Melkersson conditions with respect to a prime ideal

Aghapournahr and Melkersson introduced the notion of Melkersson condition on a Serre subcategory of the category of modules over a commutative Noetherian ring. This paper investigates the structure of a set of prime ideals satisfying the Melkersson condition on a Serre subcategory. We try to calculate members of this set for a subcategory consisting of extension modules in two given Serre subcategories. Moreover, we classify the structure of sets consisting of prime ideals satisfying the Melkersson condition over rings with a small dimension.