I read T. Y. Lam's, "A First Course in Noncommutative Rings" because I want to know an example of a division ring other than the quaternions. I read examples (1.5) and (1.6).
(1.5) I don't understand why $F=f_0+f_1+f_2+\ldots \in U(R)$ implies the constant term $f_0$ is a unit in $k$.
(1.6) Why do they do that for show that $ k ((x)) $ is division ring (take $F\cdot x^i$) ?
Thank you.