1. The problem statement, all variables and given/known data Consider the ring of polynomails in two variables over a field K: [itex]R=K[x,y] [/itex] a)Show the elements x and y are relatively prime b) Show that it is not possible to write [itex]1=p(x,y)x+q(x,y)y [/itex]with [itex]p,q \in R [/itex] c) Show R is not a principle ideal domain 2. Relevant equations None 3. The attempt at a solution I'd like to give an attempt, but I have no idea on how to start. I know that two elements a,b are relatively prime if the only integer that divides them is 1. Any help would be greatly appreciated.