On the homological dimensions of Leavitt path algebras with coefficients   in commutative rings
  In this paper, we give sharp bounds for the homological dimensions of the Leavitt path algebra $L_K(E)$ of a finite graph $E$ with coefficients in a commutative ring $K$, as well as establish a formula for calculating the homological dimensions of $L_K(E)$ when $K$ is a commutative unital algebra over a field. 
V. Lopatkin and T.G. Nam
math.RA