Row-finite Equivalents Exists Only for Graphs Having No Uncountable Emitters
نویسنده
چکیده
If E is a not-necessarily row-finite graph, such that each vertex of E emits at most countably many edges, then a desingularization F of E can be constructed as described in [3] or [7]. 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 a given graph E, a graph F having properties (1) and (2) exists (we call such a graph a row-finite equivalent) if and only if E contains no vertex v for which v emits uncountably many edges. 2000 Mathematics subject classification: Primary 16S99
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تاریخ انتشار 2009