In commutative algebra, a Rees decomposition is a way of writing a ring in terms of polynomial subrings.
They were introduced by David Rees (1956).
Suppose that a ring R is a quotient of a polynomial ring k[x1,...] 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 ηα is a homogeneous element and the d elements θi are a homogeneous system of parameters for R and ηαk[θfα+1,...,θd] ⊆ k[θ1, θfα].
This commutative algebra-related article is a stub.