  We define the extension group between an atom and an object in a locally
noetherian Grothendieck category as a module over a skew field. We show that
the dimension of the i-th extension group between an atom and an object
coincides with the i-th Bass number of the object with respect to the atom. As
an application, we give a bijection between the E-stable subcategories closed
under arbitrary direct sums and direct summands and the subsets of the atom
spectrum and show that such subcategories are also closed under extensions,
kernels of epimorphisms, and cokernels of monomorphisms. We show some
relationships to the theory of prime ideals in the case of noetherian algebras.
