The paper considers several different kinds of ideals defined by some densities. We depict relationships between Erdős-Ulam, density, matrix summability and generalized density ideals. We show that Farah's characterization when density ideals are Erdős-Ulam ideals is incorrect and try to provide a new one while showing that the conditions from the old characterization can be used to determine when density ideals have the Bolzano-Weierstrass property. Moreover, we obtain some results about a class of ideals recently established by Bose, Das and Kwela that we name simple generalized density ideals.

中文翻译：

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不同种类的密度理想

本文考虑了由某些密度定义的几种不同类型的理想。我们描述了Erdős-Ulam，密度，矩阵可加性和广义密度理想之间的关系。我们证明了当密度理想是Erdős-Ulam理想时，法拉赫的描述是不正确的，并尝试提供一个新值，同时表明旧描述中的条件可以用来确定密度理想何时具有Bolzano-Weierstrass属性。此外，我们获得了有关Bose，Das和Kwela最近建立的一类理想的一些结果，我们将其称为简单广义密度理想。