Ring generated by $S$ I know that a subring $R'$ of a ring $R$ is generated by $S\subseteq R$ if $R'$ is equal with the intersection of all subrings of $R$ those contains $S$. I want to know there is and easy way to write the elements of $R'$ in terms of the elements of $S$? Like what occurs for generated ideals in a ring.

Let $A$ be the set of all finite sums and differences of finite products of elements of $S$. Then $A$ is clearly a ring and contains $S$ and is contained in any ring that contains $S$. We conclude that $A=R'$.
