I have problems with this:
I need to prove that in the polynomial ring the radical of an ideal generated by monomials is also generated by monomials.
I found a proof on internet that uses the convex hull of the multidegrees of the monomials, but I want a proof that uses less terminology. For example, can be proved in a simple way the following:
Given a monomial $u=x^a = \prod\limits_{k = 1}^n {x_k ^{\alpha_k}}$ we define $\sqrt u = \prod\limits_{k = 1}^n {x_k }$. How can I prove that if $G(I)$ is a minimal set of generators of $I$ ( I proved that this set it's also a monomial), then the set $\left\{\sqrt u: u \in G\left(I\right) \right\}$ generates the radical of $I$?