  Let R be a quotient ring of a commutative coherent regular ring by a finitely
generated ideal. Hovey gave a bijection between the set of coherent
subcategories of the category of finitely presented R-modules and the set of
thick subcategories of the derived category of perfect R-complexes. Using this
isomorphism, he proved that every coherent subcategory of finitely presented
R-modules is a Serre subcategory. In this paper, it is proved that this holds
whenever R is a commutative noetherian ring. This paper also yields a module
version of the bijection between the set of localizing subcategories of the
derived category of R-modules and the set of subsets of Spec R which was given
by Neeman.
