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[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 η_α is a homogeneous element and the d elements θ_i are a homogeneous system of parameters for R and η_αk[θ_{f_α+1},...,θ_d] ⊆ k[θ₁, θ_{f_α}].

See also

• Stanley decomposition
• Hironaka decomposition

References