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 $Γ=(V,E)$ and an associate algebra $A,$ we construct an algebra $B=A\, wr\, L(Γ)$ with the following property: $B$ has an ideal $I$,which consists of (possibly infinite) matrices over $A$, $B/I\cong L(Γ)$, the Leavitt path algebra of the graph $Γ$. \medskip \par Let $W\subset V$ be a hereditary saturated subset of the set of vertices [1], $Γ(W)=(W,E(W,W))$ is the restriction of the graph $Γ$ to $W$, $Γ/W$ is the quotient graph [1]. Then $L(Γ)\cong L(W)$ wr $L(Γ/W)$.

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