Rings of constants of polynomial derivations and p-bases

Abstract

We present a survey of results concerning p-bases of rings of constants with respect to polynomial derivations in characteristic p > 0. We discuss characterizations of rings of constants, properties of their generators and a general characterization of their p-bases. We also focus on some special cases: one-element p-bases, eigenvector p-bases and when a ring of constants is a polynomial graded subalgebra.