Student Algebra seminar

Omar Leon Sanchez, Pure Mathematics Department, University of Waterloo

“A couple of basic questions on ideals of K[x]”

Let K be a perfect field (i.e. K = Kp), L ≥ K and x an n-tuple of indeterminates. We will intensely look at the question: If I is radical in K[x], is IL[x] radical as well? As a consequence we will be able to answer the questions:

1. If f is irreducible in K[x], can f = g2 for some g ∈ L[x]?
2. If gcd(f,g) = 1 in K[x], can it be that gcd(f,g) ̸= 1 in L[x]?

Both of these questions are easy to answer in case char K = 0 and x is a single indeterminate.