Different kinds of density ideals

The paper considers several different kinds of ideals defined by some densities. We depict relationships between Erdos-Ulam, density, matrix summability and generalized density ideals. We show that Farah's characterization when density ideals are Erdos-Ulam ideals is incorrect and try to provide anew 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 aclass of ideals recently established by Bose, Das and Kwela that we name simple generalized density ideals. (C) 2021 Elsevier Inc. All rights reserved.