let $R$ be a ring and $I$ be an index set. Suppose $x \in \bigcap Ra\_{i}$ where $a\_{i}\in R$ for every $i \in I$.
Does $x= \sum\_{i=1}^{n} r\_{i}a\_{i}$ where $r\_{i} \in R$ for every $i \in I$? i.e. is $x$ is a finite linear combination of the $a\_{i}$?