# Is every regular (excellent) scheme separated?

Sorry for one more stupid AG question. I need schemes that are regular, excellent and separated. Are these three conditions independent?

• Well, $\mathbb{A}^1 \cup_{\mathbb{A}^1-0} \mathbb{A}^1$ is smooth and non-separated. May 1 '11 at 9:15

- Separated, excellent, regular: Spec$(k)$.
- Separated, excellent, not regular: Spec$(k[\epsilon]/\epsilon^2)$.
- Separated, not excellent, not regular: Spec$(k[\epsilon_1,\epsilon_2,\ldots]/\langle\epsilon_1^2,\epsilon_2^2,\ldots\rangle$.
- Not separated, excellent, regular: Glue Spec$(\mathbb{Z})$ to itself along the complement of a closed point.