Exhibit an integral domain $R$ and a non-zero non-unit element of $R$ that is not a product of irreducibles. 
Exhibit an integral domain $R$ and a non-zero non-unit element of $R$ that is not a product of irreducibles.

My thoughts so far: I don't really have a clue. Could anyone direct me on how to think about this? I'm struggling to get my head round irreducibles.
Thanks.

how about something like $\mathbb{C}[x_1,x_2,x_3,...]$ where $x_i^2=x_{i-1}$ for $i>1$
