  Given a directed graph E we describe a method for constructing a Leavitt path
algebra $L_R(E)$ whose coefficients are in a commutative unital ring R. We
prove versions of the Graded Uniqueness Theorem and Cuntz-Krieger Uniqueness
Theorem for these Leavitt path algebras, giving proofs that both generalize and
simplify the classical results for Leavitt path algebras over fields. We also
analyze the ideal structure of $L_R(E)$, and we prove that if $K$ is a field,
then $L_K(E) \cong K \otimes_\Z L_\Z(E)$.
