Different kinds of density ideals.

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. [ABSTRACT FROM AUTHOR]