Practice problem
Let III be a homogeneous ideal of C[s,t]\mathbb{C}[s,t]C[s,t], graded by degree. If (s−t2)2∈I(s-t^2)^2\in I(s−t2)2∈I, what is the best you can say?
s2,st2,t4∈Is^2,st^2,t^4\in Is2,st2,t4∈I
s−t2∈Is-t^2\in Is−t2∈I
s,t2∈Is,t^2\in Is,t2∈I
s,t∈Is,t\in Is,t∈I
Type a concept, like “slope” or “photosynthesis”.