Morita equivalence of Leavitt path algebras over infinite graphs

The purpose of this thesis is to study the Morita equivalence of Leavitt path algebras which are defined over infinite graphs. For any graph E and any field K, we investigate conditions on E such that there is an idempotent e^2 LK(E); (e^2 = e) and the ideal generated by e is equal to LK(E). In the literature, it is shown that if R is an idempotent ring and e 2 R an idempotent element, then eRe and ReR are Morita equivalent rings. If ReR = R, then e is called a full idempotent. Hence if e in R is a full idempotent, then eRe and R are Morita equivalent rings. In this thesis, we first define a new subset of vertices of E, which we call a maximal set. Then by using this maximal set, we give the necessary and sufficient conditions on E that assure the existence of a full idempotent e in LK(E). Moreover we use a reduction algorithm on E and so we restrict the problem to a subgraph Er; r > 0 of E.