Let $S$ be a set of all even integers. According to my text book, $(S,+,\cdot)$ is a ring which is not an integral domain. It is stated as a fact without an explanation and I fail to see the reason for this.
Why the ring from above is not an integral domain?
EDIT: It can't be because of the lack of $1$ element. In the next example, $(Z,+,\cdot)$ (where $Z$ is the whole set of integers) is stated to be an integral domain.