University of Guilan Journal of Algebra and Related Topics 2345-3931 14 Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024). 2026 04 01 Characterization of rings by some filters 81 87 8823 10.22124/jart.2025.27636.1676 EN H. Mouadi Department of Mathematics and Informatics, University Ibn Zohr, Polydisciplinary Faculty, Lisima, Taroudant, Morocco A. Boua Department of Mathematics, University Sidi Mohammed Ben Abdellah-Fez, Polydisciplinary Faculty, Taza, Morocco Journal Article 2024 06 05 ‎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 $\mathcal{F}_{r}-\lim$‎. https://jart.guilan.ac.ir/article_8823_564ffe53a9facc2a3b0223a1c6549c64.pdf