Abstract

In this paper we introduce the I- and I*-convergence and divergence of nets in (ℓ)-groups. We prove some theorems relating different types of convergence/divergence for nets in (ℓ)-group setting, in relation with ideals. We consider both order and (D)-convergence.By using basic properties of order sequences, some fundamental properties, Cauchy-type characterizations and comparison results are derived.We prove that I*-convergence/divergence implies I-convergence/divergence for every ideal, admissible for the set of indexes with respect to which the net involved is directed, and we investigate a class of ideals for which the converse implication holds. Finally we pose some open problems.

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