Given a polynomial, define its support to be the set of exponent vectors of its monomials.
Given an ideal generated by monomials, define its support, supp(I), to be the monomials in the ideal.
Theorem: a polynomial p is in a monomial ideal iff each of its monomials are, iff each one is a multiple of some monomial generator.
Theorem: Monomial ideals are finitely generated.
(Both of these can be found in section 1 of the book -- we've finally made it there.)
