Esin, SongülEr, Müge Kanuni2020-05-012020-05-0120181300-00981303-6149https://doi.org/10.3906/mat-1704-116https://hdl.handle.net/20.500.12684/6353Kanuni, Muge/0000-0001-7436-039X; ESIN, SONGUL/0000-0002-1480-4566WOS: 000447946800001Let E be an arbitrary directed graph and let L be the Leavitt path algebra of the graph E over a field K. The necessary and sufficient conditions are given to assure the existence of a maximal ideal in L and also the necessary and sufficient conditions on the graph that assure that every ideal is contained in a maximal ideal are given. It is shown that if a maximal ideal M of L is nongraded, then the largest graded ideal in M, namely gr(M), is also maximal among the graded ideals of L. Moreover, if L has a unique maximal ideal M, then M must be a graded ideal. The necessary and sufficient conditions on the graph for which every maximal ideal is graded are discussed.en10.3906/mat-1704-116info:eu-repo/semantics/openAccessLeavitt path algebrasarbitrary graphsmaximal idealsArticle42520812090WOS:000447946800001Q2Q3