  Derived decompositions of abelian categories are introduced in internal terms
of abelian subcategories to construct semi-orthogonal decompositions (or
Bousfield localizations, or hereditary torsion pairs) in various derived
categories of abelian categories. We give a sufficient condition for arbitrary
abelian categories to have such derived decompositions and show that it is also
necessary for abelian categories with enough projectives and injectives. For
bounded derived categories, we describe which semi-orthogonal decompositions
are determined by derived decompositions. The necessary and sufficient
condition is then applied to the module categories of rings: localizing
subcategories, homological ring epimorphisms, commutative noetherian rings and
nonsingular rings. Moreover, for a commutative noetherian ring of Krull
dimension at most $1$, a derived stratification of its module category is
established.
