行有限等价只存在于行可数图中
Row-finite equivalents exist only for row-countable graphs
摘要：
如果$E$是不一定行有限的图，使得$E$的每个顶点发出至多可数条边，则可以构造$E$的{ \it去奇异化} $F$（例如参见（1）G. Abrams，G. Aranda Pino，Leavitt path algebras of arbitrary graphs，Houston J. Math 34（2）（2008），423-442，or（2）I. Raeburn，“Graph algebras”. CBMS Regional Conference Series in Mathematics 103，Conference Board of the Mathematical Sciences，Washington，DC，2005，ISBN 0-8218-3660-9）。去奇异化过程已被有效地用于建立不一定行有限图的莱维特路代数的各种特征。$E$的这种去奇异化$F$具有以下性质：（1）$F$是行有限的，（2）Leavitt路代数$L(E)$和$L(F)$是Morita等价的.我们证明了对于任意图$E$，存在具有性质（1）和（2）的图$F$（我们称这样的图$F$为\emph{row-finite equivalent of} $E$）当且仅当$E$是行可数的;也就是说，$E$不包含$v$发出不可数条边的顶点$v$。
英文摘要：
If $E$ is a not-necessarily row-finite graph, such that each vertex of $E$ emits at most countably many edges, then a {\it desingularization} $F$ of $E$ can be constructed (see e.g. (1) G. Abrams, G. Aranda Pino, Leavitt path algebras of arbitrary graphs, Houston J. Math 34(2) (2008), 423-442, or (2) I. Raeburn, "Graph algebras". CBMS Regional Conference Series in Mathematics 103, Conference Board of the Mathematical Sciences, Washington, DC, 2005, ISBN 0-8218-3660-9). The desingularization process has been effectively used to establish various characteristics of the Leavitt path algebras of not-necessarily row-finite graphs. Such a desingularization $F$ of $E$ has the properties that: (1) $F$ is row-finite, and (2) the Leavitt path algebras $L(E)$ and $L(F)$ are Morita equivalent. We show here that for an arbitrary graph $E$, a graph $F$ having properties (1) and (2) exists (we call such a graph $F$ a \emph{row-finite equivalent of} $E$) if and only if $E$ is row-countable; that is, $E$ contains no vertex $v$ for which $v$ emits uncountably many edges.
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