Rees decomposition

In commutative algebra, a Rees decomposition is a way of writing a ring in terms of polynomial subrings. They were introduced by .
Definition.
Suppose that a ring "R" is a quotient of a polynomial ring "k"["x"1...] over a field by some homogeneous ideal. A Rees decomposition of "R" is a representation of "R" as a direct sum (of vector spaces)
where each "η""α" is a homogeneous element and the "d" elements "θ""i" are a homogeneous system of parameters for "R" and
"η""α""k"["θ""f""α"+1...,"θ""d"] ⊆ "k"["θ"1, "θ""f""α"].