  Aghapournahr and Melkersson introduced the notion of Melkersson condition on
a Serre subcategory of the module category over a commutative noetherian ring.
This paper investigates the structure of set of prime ideals satisfying a
Melkersson condition on a Serre subcategory. We try to calculate members of a
set of these prime ideals for a subcategory consisting of extension modules in
two given Serre subcategories of the module category. Meanwhile, we classify
the structure of set of prime ideals satisfying a Melkersson condition over a
0-dimensional ring, a 1-dimensional local ring, and a 2-dimensional local
domain.
