Wreath products by a Leavitt path algebra

We introduce ring theoretic constructions that are similar to the construction of wreath product of groups. In particular, for a given graph $\mathrm{\Gamma }=(V,E)$ and an associate algebra $A,$ we construct an algebra $B=A, wr, L(\Gamma)$withthefollowingproperty:$B$hasanideal$I$,which consists of (possibly infinite) matrices over $A$, $B\mathrm{/}I\cong L(\mathrm{\Gamma })$, the Leavitt path algebra of the graph $\mathrm{\Gamma }$. \medskip \par Let $W\subset V$ be a hereditary saturated subset of the set of vertices [1], $\mathrm{\Gamma }(W)=(W,E(W,W))$ is the restriction of the graph $\mathrm{\Gamma }$ to $W$, $\mathrm{\Gamma }\mathrm{/}W$ is the quotient graph [1]. Then $L(\mathrm{\Gamma })\cong L(W)$ wr $L(\mathrm{\Gamma }\mathrm{/}W)$.