We 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.

中文翻译：

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Leavitt Path代数中的最大理想

我们确定了Leavitt路径代数中的最大理想：最大的局部左/右Artinian（这是最大的半简单的），最大的局部左/右noetherian，没有最小的幂等性，最大的交换，以及最大的纯无穷大。最后一个理想被描述为纯粹无限的简单块加上纯粹无限的非简单和不可分解块的直接总和。还研究了这些理想的环同构下的不变性。