Abstract
We introduce ring theoretic constructions that are similar to the construction of wreath product of groups [M. Kargapolov and Y. Merzlyakov, Fundamentals of the Theory of Groups (Springer-Verlag, New York, 1979)]. In particular, for a given graph Gamma = (V, E) and an associate algebra A, we construct an algebra B = A wr L(Gamma) with the following property: B has an ideal I, which consists of (possibly infinite) matrices over A, B/I congruent to L(Gamma), the Leavitt path algebra of the graph Gamma. Let W subset of V be a hereditary saturated subset of the set of vertices [G. Abrams and G. Aranda Pino, The Leavitt path algebra of a graph, J. Algebra 293(2) (2005) 319-334], Gamma(W) = (W, E(W, W)) is the restriction of the graph Gamma to W, Gamma/W is the quotient graph [G. Abrams and G. Aranda Pino, The Leavitt path algebra of a graph, J. Algebra 293(2) (2005) 319-334]. Then L(Gamma) congruent to L(W) wr L(Gamma/W). As an application we use wreath products to construct new examples of (i) affine algebras with non-nil Jacobson radicals, (ii) affine algebras with non-nilpotent locally nilpotent radicals.