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We examine relationship between ideal convergence and matrix summability in the realm of bounded and unbounded sequences.

Abstract. We say that an ideal I on ω is homogeneous, if its restriction to any I-positive subset of ω is isomorphic to I. The paper investigates basic properties of this notion -we give examples of homogeneous ideals and present some applications to topology and ideal convergence. Moreover, we answer questions related to our research posed in [1].