Characterization of rings by some filters

‎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.

کلیدواژه ها:

‎Direct product‎ ، ‎Direct sum‎ ، ‎Frechet filter‎ ، ‎\mathcal{F}_{r}-\lim