R[X,Y] polynomial ring

I want to show that R[x,y] is not a principal ideal domain,
So i'm trying to construct an ideal which is not principal

i do not fully understand what my text book means by:

R[X,Y]
Let I=(x,y)={XP(X,Y) + YQ(X,Y)}
={a_0 + a_1X _ a_2X^2+......... : a_0=0}
( i dont understand why a_0=0?)

then
X + Y +X^3 + XY^14

If I=R[X,Y]s(x,y)
X,Y elements of I
s(x,y)|x and s(x,y)|y

0 does not equal s(x,y)=a_0
s(x,y) element of I Contradiction
therefore Not PID

If anyone can shed light on understanding this proof, or examples why R[X,Y]
is not a PID it with be greatly appreciated

Thanks once again


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