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In this paper we present some different types of ideal convergence/divergence and of ideal continuity for Riesz space-valued functions, and prove some basic properties and comparison results. We investigate the relations among different modes of ideal continuity and present a characterization of the ( AP )-property for ideals of an abstract set Λ. Finally we pose some open problems.

Modes of ideal continuity and the additive property in the Riesz space setting