Ideal convergence and divergence of nets in $(\ell )$-groups
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 1073-1083.

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In this paper we introduce the ${\mathcal I}$- and ${\mathcal I}^*$-convergence and divergence of nets in $(\ell )$-groups. We prove some theorems relating different types of convergence/divergence for nets in $(\ell )$-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 ${\mathcal I}^*$-convergence/divergence implies ${\mathcal I}$-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.
DOI : 10.1007/s10587-012-0064-z
Classification : 28B10, 28B15, 54A20
Mots-clés : net; $(\ell )$-group; ideal; ideal order; $(D)$-convergence; ideal divergence 
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     title = {Ideal convergence and divergence of nets in $(\ell )$-groups},
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Boccuto, Antonio; Dimitriou, Xenofon; Papanastassiou, Nikolaos. Ideal convergence and divergence of nets in $(\ell )$-groups. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 1073-1083. doi : 10.1007/s10587-012-0064-z. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0064-z/

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