Let $R$ be a ring and $S$ be a subring of $R$. Suppose that $R$ does not have unity, but $S$ does. Let $1_S$ be the unity of S. Show that $1_S$ is a zero divisor of $R$.
I've been stuck on this for a bit, and I'm not sure how to approach it. I know how to show that if $R$ has unity, then every element of S is a zero divisor, but I can't seem to nail this case. Any help or guidance would be helpful.