I found a problem in this paper on Example 1.
Let $R$ be a commutative ring and $S$ a multiplicative subset of $R$ such that $R$ is $S$-Noetherian but not Noetherian. (For example, one may take $R$ to be a non-Noetherian integral domain with $S = R \backslash \{0\}$). In those paper said that such example can be found in here.
But in another version of this paper, said that such example can be found here on Example 3.1. I've read this example. Why those example is $S$-Noetherian but not Noetherian? How to prove that non-Noetherian integral domain with $S = R \backslash \{0\}$ is $S$-Noetherian but not Noetherian ? How to find another example?