Must PID contain 1? Must PID contain 1? My concern arises when i consider the gcd of say a and b in the PID. Since it is a PID, it is generated by one element say k. k obviously $\in (k)$. However, if PID does not contain 1, then i can't write $k = k \cdot 1$, can 1? So is it true that then k must be equal to $k = k \cdot q$ for some $q \in$ PID. I find this kind of weird. Am I misunderstanding anything?

A PID is in particular a domain, which is required to contain a $1$. 
