/sci/ - Science & Math

[math]R =\langle \{ ax^b : a \in \mathbb{C}, b \in \mathbb{Q}^+ \} \rangle[/math] (complex polynomials on one variable with nonnegative rational powers) works innit? Not noetherian because we can just get the ideal generated by a smaller [math]b[/math], but the spectrum satisfies the condition because it only has only one non-trivial prime ideal, right?