Let Z_(p) be the localization of the integers at some prime ideal (p). Polynomial rings or power series rings in n variables have a natural N^n-multigrading given by multidegree in each of the variables. Over a field, the homogeneous elements under this multigrading are just monomials, but over Z_(p) the homogeneous elements are "p-monomials": the product of a monomial with a power of the prime p. Surprisingly, many of the nice computational lemmas from the monomial setting can be replicated for p-monomials. I will discuss the properties of p-monomials and show some examples of rings constructed using p-monomials.