Cam, VuralGil Canto, CristobalKanuni, MugeSiles Molina, Mercedes2021-12-012021-12-0120201660-54461660-5454https://doi.org/10.1007/s00009-020-1486-8https://hdl.handle.net/20.500.12684/10711We identify the largest ideals in Leavitt path algebras: the largest locally left/right artinian (which is the largest semisimple one), the largest locally left/right noetherian without minimal idempotents, the largest exchange, and the largest purely infinite. This last ideal is described as a direct sum of purely infinite simple pieces plus purely infinite non-simple and non-decomposable pieces. The invariance under ring isomorphisms of these ideals is also studied.en10.1007/s00009-020-1486-8info:eu-repo/semantics/openAccessLeavitt path algebrasocleextreme cycleline pointpurely infinite idealCyclesSocleArticle1722-s2.0-85079825094WOS:000517611200006Q2Q2