Content of a Polynomial (Lang) Referring to Lang's Algebra p. 181, let $A$ be a factorial ring and $K$ its field of fractions. It is clear by definition, that the content of $f(x) \in K[x]$ is an element of $A$. In the beginning of the paragraph above Theorem 2.1 it is mentioned that if $b \in K, \, b \neq 0$, then $cont(bf)=b \cdot cont(f)$. But then $b \cdot cont(f)$ might not be inside $A$. Is this a typo or am i missing something? Thanks.

With Lang's definition, I don't think that the content is necessarily an element of A. In his notation, it is perfectly fine for $ord_p a_i$ to be negative.