Characterization of rings by some filters

Mouadi, H.; Boua, A.

doi:10.22124/jart.2025.27636.1676

Characterization of rings by some filters

Articles in Press

Document Type : Research Paper

Authors

H. Mouadi ¹
A. Boua ²

¹ Department of Mathematics and Informatics, University Ibn Zohr, Polydisciplinary Faculty, Lisima, Taroudant, Morocco

² Department of Mathematics, University Sidi Mohammed Ben Abdellah-Fez, Polydisciplinary Faculty, Taza, Morocco

10.22124/jart.2025.27636.1676

Abstract

‎Let $R=\prod_{i\in I}R_{i}$ be the product of an infinite family of rings $\{R_{i}\}_{i\in I}$‎. ‎In this study‎, ‎we investigate the direct sum $\bigoplus_{i\in I}R_{i}$‎. ‎Special attention is paid to the relationship between the ideal $\bigoplus_{i\in I}R_{i}$ and the $\mathcal{F}_{r}$ Frechet filter in $I$‎, ‎also we show a new characterization of $\bigoplus_{i\in I}R_{i}$ by the $\mathcal{F}_{r}-\lim$‎.

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