If we define , how would I show that 2, 3, and are all irreducible?
I have shown that none of these are units of .
For example, if I assume that , I need to show that at least one of x and y is a unit. Obviously if 2 = 2 x 1 = 1 x 2, then 1 is a unit, but how do I show that there are no other factorisations of 2 in ?
Thanks for help!