  In this paper, we explore the nature of central idempotents of Schur rings
over finite groups. We introduce the concept of a lattice Schur ring and
explore properties of these kinds of Schur rings. In particular, the primitive,
central idempotents of lattice Schur rings are completely determined. For a
general Schur ring $S$, $S$ contains a maximal lattice Schur ring, whose
central, primitive idempotents form a system of pairwise orthogonal, central
idempotents in $S$. We show that if $S$ is a Schur ring with rational
coefficients over a cyclic group, then these idempotents are always primitive
and are spanned by the normal subgroups contained in $S$. Furthermore, a
Wedderburn decomposition of Schur rings over cyclic groups is given. Some
examples of Schur rings over non-cyclic groups will also be explored.
