What does it mean to be "working over a field?" I thought that the coefficients of the polynomial had to be members of a field.
I get it. That's kind of interesting.
Does one need the Riemann sphere to define 0 as a member of C?
How can we have divisors without being able to divide? What is this new (to me) definition of divisor? Why do you only list 4 and 2? I thought that 0/anything = 0. Is it that 0/2 = 4 and 0/4 = 2? Is that true? If so, that's wierd.
What is a "omthe poly?"
When we say "divide," do we always assume that there is no remainder? So, basically, by saying "p divides r-s," that is another way of saying that "p is a factor of r-s?"
This looks like Chinese to me (and I am not oriental).
Thanks for the reference. I will try to motivate myself through it (first I have to motivate myself to the library).
I realize that this addresses my question with a counterexample, so I do not dispute it. But, for the sake of future discussion, will infinite order polynomials be relevant? If so, then this seems like an example to show that not even the complex field is alg closed.