Hey there,

LetRbe the ring consisting of the power series of the form

$\displaystyle \sum_{n=1}^{\infty}a_{n}x^{\alpha_n}$ where $\displaystyle a_n \in \mathbb{R}$ and $\displaystyle 0 < \alpha_1 < \alpha_2 < \cdots $ are real numbers so that $\displaystyle \lim_{x\to\infty}\alpha_n = \infty$.

I want to show that R is an integral domain without a maximal ideal. But I don't see how to start...